  
  [1X1 [33X[0;0YIntroduction to the [5XAtlasRep[105X[101X[1X Package[133X[101X
  
  [33X[0;0YThe  aim  of the [5XGAP[105X 4 package [5XAtlasRep[105X is to provide a link between [5XGAP[105X and
  databases such as the [5XATLAS[105X of Group Representations [WWT+], which comprises
  generating  permutations  and  matrices  for  many almost simple groups, and
  information  about  their  maximal  subgroups.  This  database  is available
  independent of [5XGAP[105X at[133X
  
  [33X[0;0Y[7Xhttp://atlas.math.rwth-aachen.de/Atlas/v3[107X.[133X
  
  [33X[0;0YThe  [5XAtlasRep[105X  package consists of this database (see Section [14X1.1[114X) and a [5XGAP[105X
  interface  (see  Section [14X1.2[114X); the latter is extended by further information
  available via the internet (see Section [14X4.3[114X).[133X
  
  [33X[0;0YThis package manual has the following parts.[133X
  
  [8XA tutorial[108X
        [33X[0;6Ygives  an  overview  how the functions of the package can be used, see
        Chapter [14X2[114X.[133X
  
  [8XUser interface functions[108X
        [33X[0;6Yare described in Chapter [14X3[114X.[133X
  
  [8XCustomizations of the package[108X
        [33X[0;6Yare described in Chapter [14X4[114X.[133X
  
  [8XInformation how to extend the database[108X
        [33X[0;6Ycan be found in Chapter [14X5[114X.[133X
  
  [8XMore technical information[108X
        [33X[0;6Ycan  be  found  in  the  chapters [14X6[114X  (concerning  [5XGAP[105X objects that are
        introduced  by  the  package)  and [14X7[114X  (concerning global variables and
        sanity checks).[133X
  
  
  [1X1.1 [33X[0;0YThe [5XATLAS[105X[101X[1X of Group Representations[133X[101X
  
  [33X[0;0YThe [5XATLAS[105X of Group Representations  [WWT+] consists of matrices over various
  rings, permutations, and shell scripts encoding so-called black box programs
  (see  [Nic06]  and  Section [14X6.2[114X).  Many  of  these scripts are straight line
  programs  (see [BSWW01],  [SWW00],  and [14X'Reference: Straight Line Programs'[114X)
  and straight line decisions (see Section [14X6.1[114X). These programs can be used to
  compute  certain  elements  in  a  group  [22XG[122X  from  its  standard  generators
  (see [Wil96] and Section [14X3.3[114X) for example generators of maximal subgroups of
  [22XG[122X or representatives of conjugacy classes of [22XG[122X.[133X
  
  [33X[0;0YThe [5XATLAS[105X 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).[133X
  
  [33X[0;0YThe  information  was  computed  and composed using computer algebra systems
  such  as  [5XMeatAxe[105X  (see [Rin]),  Magma  (see [CP96]),  and  [5XGAP[105X  (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  bibliographies in [CCN+85] and [BN95]
  which             are             available             online            at
  [7Xhttp://www.math.rwth-aachen.de/~Thomas.Breuer/atlasrep/bibl[107X.[133X
  
  [33X[0;0YIf you use the [5XATLAS[105X of Group Representations to solve a problem then please
  send  a  short  email to [7Xmailto:R.A.Wilson@qmul.ac.uk[107X about it. The [5XATLAS[105X of
  Group Representations database should be referenced with the entry [WWT+] in
  the bibliography of this manual.[133X
  
  [33X[0;0YIf  your  work  made use of functions of the [5XGAP[105X interface (see Section [14X1.2[114X)
  then you should also reference this interface, using the information printed
  by the [5XGAP[105X function [2XCite[102X ([14XReference: Cite[114X).[133X
  
  [33X[0;0YFor  referencing  the  [5XGAP[105X  system  in general, use the entry [GAP19] in the
  bibliography of this manual, see also [7Xhttp://www.gap-system.org[107X.[133X
  
  
  [1X1.2 [33X[0;0YThe GAP Interface to the [5XATLAS[105X[101X[1X of Group Representations[133X[101X
  
  [33X[0;0YThe  [5XGAP[105X  interface  to  the  [5XATLAS[105X  of  Group  Representations  consists of
  essentially two parts.[133X
  
  [30X    [33X[0;6YFirst,  there  is  the  [13Xuser interface[113X which allows the user to get an
        overview  of  the  contents of the database, and to access the data in
        [5XGAP[105X  format;  this  is  described in Chapter [14X3[114X. Advanced users may add
        their own data to the database, this is described in Chapter [14X5[114X.[133X
  
  [30X    [33X[0;6YSecond,  there  is [13Xadministrational information[113X, which covers also the
        declaration  of  [5XGAP[105X 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  [10XC[110X-[5XMeatAxe[105X  standalone  (see [Rin]);  this  is
        described in Chapter [14X7[114X.[133X
  
  [33X[0;0YInformation  concerning  the  [10XC[110X-[5XMeatAxe[105X,  including the manual [Rin], can be
  found at[133X
  
  [33X[0;0Y[7Xhttp://www.math.rwth-aachen.de/~MTX[107X[133X
  
  [33X[0;0YThe  interface  and  this manual have been provided by Thomas Breuer, except
  for  the  interpreter for black box programs (see Section [14X6.2[114X), which is due
  to  Simon  Nickerson.  Comments,  bug  reports,  and hints for improving the
  interface can be sent to [7Xmailto:sam@math.rwth-aachen.de[107X.[133X
  
  
  [1X1.3 [33X[0;0YWhat's New in [5XAtlasRep[105X[101X[1X, Compared to Older Versions?[133X[101X
  
  
  [1X1.3-1 [33X[0;0YWhat's New in Version 2.1.6? (October 2022)[133X[101X
  
  [33X[0;0YThe  package  now requires the [5Xutils[105X package [BGH+22], and uses its [2XDownload[102X
  ([14XUtils:  Download[114X)  function  for  downloading remote files. The former user
  preference  [10XFileTransferTool[110X of the [5XAtlasRep[105X package is no longer supported;
  it had been used in older versions to distinguish between different download
  tools.[133X
  
  [33X[0;0YA  method  for  [2XConjugacyClasses[102X ([14XReference: ConjugacyClasses attribute[114X) has
  been   added   that  uses  a  straight  line  program  for  computing  class
  representatives  of  a  group that has been created with [2XAtlasGroup[102X ([14X3.5-8[114X),
  provided  such a program is available. Thanks to Frank Lübeck for suggesting
  this.[133X
  
  
  [1X1.3-2 [33X[0;0YWhat's New in Version 2.1.5? (August 2022)[133X[101X
  
  [33X[0;0YTwo  bugs  concerning  local  file  permissions and the handling of download
  failures  were  fixed.  Thanks  to  Frank  Lübeck  and  Fabian  Zickgraf for
  reporting these problems.[133X
  
  
  [1X1.3-3 [33X[0;0YWhat's New in Version 2.1.4? (August 2022)[133X[101X
  
  [33X[0;0YA few changes in the code for downloading files were needed in order to make
  some CI tests happy.[133X
  
  
  [1X1.3-4 [33X[0;0YWhat's New in Version 2.1.3? (August 2022)[133X[101X
  
  [33X[0;0YThe server address for the core part of the database has changed.[133X
  
  [33X[0;0YAdditional  table  of  contents  files  are  now  available,  which  contain
  checksums  in  SHA256  format  instead  of the checksums computed by [2XCrcFile[102X
  ([14XReference:  CrcFile[114X)  and  [2XCrcString[102X  ([14XReference: CrcString[114X). Note that the
  latter values can be interpreted only by [5XGAP[105X.[133X
  
  [33X[0;0YFor  [22X364[122X  representations, the corresponding characters have been identified
  and   can   thus   be   used   for   accessing  these  representations  with
  [2XOneAtlasGeneratingSetInfo[102X ([14X3.5-6[114X), see [2XDisplayAtlasInfo[102X ([14X3.5-1[114X).[133X
  
  
  [1X1.3-5 [33X[0;0YWhat's New in Version 2.1.2? (March 2022)[133X[101X
  
  [33X[0;0YNot much.[133X
  
  [33X[0;0YThe  release  of  Version 2.1.2 was necessary for technical reasons: Now the
  testfile  mentioned  in [11XPackageInfo.g[111X exits [5XGAP[105X in the end, and the external
  links   in   the   package   documentation  were  corrected  (the  links  in
  version 2.1.1 pointed to a wrong directory).[133X
  
  
  [1X1.3-6 [33X[0;0YWhat's New in Version 2.1.1? (February 2022)[133X[101X
  
  [30X    [33X[0;6YThe  new function [2XEvaluatePresentation[102X ([14X3.5-11[114X) computes the images of
        the relators of a presentation (see Section [14X6.1-7[114X).[133X
  
  [30X    [33X[0;6YThe new function [2XStandardGeneratorsData[102X ([14X3.5-12[114X) allows one to compute
        standard  generators from given generators, provided a recipe for that
        task  (a  [21Xfind[121X  straight  line  program)  for the group in question is
        available.[133X
  
  [30X    [33X[0;6YThe function [2XAtlasGroup[102X ([14X3.5-8[114X) sets known information about the group
        and the representation, such as [2XIsPrimitive[102X ([14XReference: IsPrimitive[114X).[133X
  
        [33X[0;6Y(Thanks to Steve Linton for suggesting this feature.)[133X
  
  [30X    [33X[0;6YThe  function  [2XResultOfBBoxProgram[102X  ([14X6.2-4[114X)  now  admits  an  optional
        argument,  which  is used as options record in calls to [2XRunBBoxProgram[102X
        ([14X6.2-3[114X).[133X
  
  [30X    [33X[0;6YThe  new  user  preference  [10X"AtlasRepJsonFilesAddresses"[110X  (see Section
        [14X4.2-14[114X)   allows  one  to  use  Json  format  data  files  for  matrix
        representations  in  characteristic  zero,  which  in  turn  makes  it
        possible  to  create  the matrices over prescribed fields, for example
        fields returned by [2XAlgebraicExtension[102X ([14XReference: AlgebraicExtension[114X).
        The  information  stored in the table of contents file about the field
        of  entries  of  the matrix representations has been extended by a [5XGAP[105X
        independent description of this field and the defining polynomial used
        in the Json format data files.[133X
  
  [30X    [33X[0;6YWhen  the  value  of the user preference [10X"AtlasRepDataDirectory"[110X is an
        empty  string then data files that are fetched from remote servers are
        read  into the [5XGAP[105X session without storing the files. (An advantage is
        that  one  need  not  care about where one has permissions for storing
        files.  A disadvantage is of course that one has to fetch a file again
        whenever it is needed.)[133X
  
  
  [1X1.3-7 [33X[0;0YWhat's New in Version 2.1.0? (May 2019)[133X[101X
  
  [33X[0;0YThe main differences to earlier versions concern extensions of the available
  data.  Up  to  now, such extensions were possible only in the sense that one
  could  notify  certain  [13Xlocally  available files[113X to the package's functions.
  With  this version, it becomes possible to notify also [13Xremote data files[113X, i.
  e., data files which have to be downloaded before they can be read into [5XGAP[105X,
  in  the  same  way  as the data from the [5XATLAS[105X of Group Representations. Two
  extensions  of  this  kind  become automatically available with this package
  version, see Section [14X5.1[114X for details.[133X
  
  [33X[0;0YThus  the focus of the package has changed. In earlier versions, it provided
  a  [5XGAP[105X  interface to the data in the [5XATLAS[105X of Group Representations, whereas
  now  this  database  is  regarded  as  one  collection (the [21Xcore part[121X) among
  others.  Where  applicable,  the package manual tries to distinguish between
  general data available to the [5XAtlasRep[105X functions and the data from the [5XATLAS[105X
  of Group Representations.[133X
  
  [33X[0;0YIn  order to provide this new functionality, the following changes have been
  implemented.  Note that some are [13Xincompatible changes[113X, compared with earlier
  versions of the package.[133X
  
  [30X    [33X[0;6YThe  format  of  the  [10Xidentifier[110X components of the records returned by
        [2XAtlasGenerators[102X  ([14X3.5-3[114X), [2XAtlasProgram[102X ([14X3.5-4[114X), etc., has been changed
        for  those data that belong to extensions, see [14X7.7[114X. In the new format,
        the  name  of  the extension is not added to the group name but to the
        individual filenames; this allows for example the combination of files
        from  the  core  database  and  from  extensions  in  one  identifier.
        Functions  for  converting  between  the  old  and  the new format are
        available, see [2XAtlasRepIdentifier[102X ([14X7.7-1[114X).[133X
  
  [30X    [33X[0;6YThe  records  returned  by [2XAtlasGenerators[102X ([14X3.5-3[114X) etc. contain also a
        component  [10Xcontents[110X,  with  value  the  identifier  of the part of the
        database to shich the generators belong.[133X
  
  [30X    [33X[0;6YThe  tables  of  contents of the [5XATLAS[105X of Group Representations and of
        extensions  are  no longer stored in the form of sequences of calls to
        [5XGAP[105X  functions.  Instead, each table of contents is defined via a JSON
        format  file,  see [14X6.4[114X. In particular, the file [11Xatlasprm.json[111X replaces
        the former [11Xgap/atlasprm.g[111X.[133X
  
        [33X[0;6YTwo  advantages  of  this  change  are that there is no danger to call
        unwanted  [5XGAP[105X  functions  when  such  files  (which are expected to be
        available  in  the  world  wide  web)  get  evaluated,  and  that  the
        information  is independent of [5XGAP[105X –note that [5XMeatAxe[105X format files and
        straight line programs can be used by other program systems as well.[133X
  
  [30X    [33X[0;6YThe  functions  [10XReloadAtlasTableOfContents[110X, [10XStoreAtlasTableOfContents[110X,
        and [10XReplaceAtlasTableOfContents[110X are no longer available. They had been
        intended  for  updating  the  table  of contents of the [5XATLAS[105X of Group
        Representations,  but  it  has  turned  out  that this was in fact not
        useful.[133X
  
  [33X[0;0YThe second major change concerns the handling of user parameters.[133X
  
  [30X    [33X[0;6Y[5XGAP[105X's   general  [13Xuser  preferences[113X  mechanism  (see  [2XSetUserPreference[102X
        ([14XReference:  SetUserPreference[114X))  has been used since version 1.5.1 of
        the  package  for  dealing  with  certain customizations of [5XAtlasRep[105X's
        behaviour,  concerning  the  paths  of data directories and two issues
        with [5XMeatAxe[105X format files.[133X
  
        [33X[0;6YNow  this  mechanism  is  used  in  more cases, see Section [14X4.2[114X for an
        overview.  The  new user preferences replace certain components of the
        record  [2XAtlasOfGroupRepresentationsInfo[102X  ([14X7.1-5[114X) that were recommended
        in  earlier  versions  of  the package. These components are currently
        still  available  but  are  no longer used by the package's functions.
        Also  the global variable [10XATLASREP_TOCFILE[110X is no longer supported, use
        the  user  preference  [10XAtlasRepTOCData[110X  instead,  see  Section  [14X4.2-3[114X.
        Analogously, use the user preference [10XHowToReadMeatAxeTextFiles[110X instead
        of the no longer available [10XCMeatAxe.FastRead[110X.[133X
  
        [33X[0;6YThe  switch  to  user preferences is an [13Xincompatible change[113X if you are
        used  to  change  the  values  of  these  components in your code, for
        example  in  your  [11Xgaprc[111X  file,  see [14X'Reference: The gap.ini and gaprc
        files'[114X. All assignments to these components should be changed to calls
        of [2XSetUserPreference[102X ([14XReference: SetUserPreference[114X).[133X
  
        [33X[0;6YAnother  consequence  of  this  change  is  that  the  former function
        [10XAtlasOfGroupRepresentationsUserParameters[110X  of the package is no longer
        supported, use [2XShowUserPreferences[102X ([14XReference: ShowUserPreferences[114X) or
        [2XBrowseUserPreferences[102X  ([14XBrowse:  BrowseUserPreferences[114X)  with argument
        [10X"AtlasRep"[110X instead.[133X
  
  [33X[0;0YFinally, the following improvements have been added.[133X
  
  [30X    [33X[0;6YStraight  line  programs  for computing generators of normal subgroups
        can  now  be  fetched  with  [2XAtlasProgram[102X  ([14X3.5-4[114X), using the argument
        [10X"kernel"[110X.  The  available  programs  of  this  type  are  shown in the
        [2XDisplayAtlasInfo[102X  ([14X3.5-1[114X)  overview  for  a  group. More than [22X200[122X such
        programs are available in a new data directory [11Xdatapkg[111X of the package.
        If  fact,  this  collection  of  files  is part of an extension of the
        database that is distributed together with the package.[133X
  
        [33X[0;6YIn  earlier versions of the package, this kind of information had been
        available only implicitly; it had been stored via [10XAGR.KERPRG[110X, which is
        not supported anymore.[133X
  
  [30X    [33X[0;6Y[2XAtlasProgram[102X  ([14X3.5-4[114X)  supports more variants of arguments: [10X"contents"[110X
        can  be  used  to  list  the available data extensions, [10X"contents"[110X and
        [10X"version"[110X  can  be  used to restrict the data under consideration, and
        one  can  request  a program for computing [13Xstandard[113X generators of some
        maximal  subgroup, not just generators (provided that this information
        is available).[133X
  
        [33X[0;6YThe  information  about the version of straight line programs is shown
        by  [2XDisplayAtlasInfo[102X  ([14X3.5-1[114X), as well as the availability of straight
        line programs for computing standard generators of maximal subgroups.[133X
  
        [33X[0;6YMaking  this  information  more  explicit has the side-effect that the
        access   to   the   [5XAtlasRep[105X   data   with   [2XBrowseAtlasInfo[102X  ([14XBrowse:
        BrowseAtlasInfo[114X)  is both safer and simpler, if at least version 1.8.6
        of   the   [5XBrowse[105X  package  is  available.  (For  that,  the  function
        [10XAGR.InfoPrgs[110X  has  been extended such that also the [10Xidentifier[110X records
        are included in the result.)[133X
  
  [30X    [33X[0;6YStraight  line programs for computing [13Xstandard[113X generators of a maximal
        subgroup,  if available, can now be fetched with [2XAtlasProgram[102X ([14X3.5-4[114X),
        using the argument [10X"maxstd"[110X.[133X
  
  [30X    [33X[0;6YThe  function  [2XAtlasRepInfoRecord[102X  ([14X3.5-10[114X) now admits a group name as
        its  argument,  and  then  returns information about the group and its
        maximal   subgroups;   this   information  had  been  used  before  by
        [2XDisplayAtlasInfo[102X   ([14X3.5-1[114X),  but  it  had  not  been  programmatically
        accessible.[133X
  
  [30X    [33X[0;6YThe  sanity  checks for the data (see Section [14X7.9[114X) have been extended,
        in  particular  they  can  be applied also to data extensions. To some
        extent,  these  checks can be used also to derive new information; the
        code  for  that  should  be  regarded  as  heuristic and experimental,
        runtimes  and  space  requirements  may be large, depending on the new
        data to be examined.[133X
  
  [30X    [33X[0;6YDifferent  header  formats  are now supported when reading and writing
        [5XMeatAxe[105X  format  files,  see  Section  [14X4.2-8[114X, and one can set a global
        default for the creation of mode 2 [5XMeatAxe[105X files, see Section [14X4.2-9[114X.[133X
  
  [30X    [33X[0;6YThe  function  [2XMeatAxeString[102X  ([14X7.3-2[114X) admits also an integer matrix as
        argument.[133X
  
  [30X    [33X[0;6YThe function [2XCMtxBinaryFFMatOrPerm[102X ([14X7.3-4[114X) admits an optional argument
        [3Xbase[103X,  in order to write [5XMeatAxe[105X format files that contain either zero
        based or one based permutations.[133X
  
  [30X    [33X[0;6YThe  meaningless  lines about [22Xp[122X-modular representations of groups with
        nontrivial [22Xp[122X-core have been removed from the file [11Xgap/mindeg.g[111X.[133X
  
  
  [1X1.3-8 [33X[0;0YWhat's New in Version 1.5.1? (March 2016)[133X[101X
  
  [30X    [33X[0;6YThe  paths  of  the directories where downloaded data files get stored
        are  now  customizable,  see  Section  [14X4.2-2[114X. 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 [5XGAP[105X
        or  of  the [5XAtlasRep[105X package gets installed.) Thanks to Bill Allombert
        for pointing out this problem.[133X
  
  [30X    [33X[0;6YThe   information   about   data   files   from  the  [5XATLAS[105X  of  Group
        Representations  has  been  extended  by  [2XCrcFile[102X ([14XReference: CrcFile[114X)
        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.[133X
  
  [30X    [33X[0;6YWhenever [2XStringFile[102X ([14XGAPDoc: StringFile[114X) is called by functions of the
        package, this happens in the wrapper function [10XAGR.StringFile[110X, in order
        to  replace  occasional  line  breaks  of  the  form  [10X"\r\n"[110X  by [10X"\n"[110X.
        Apparently  it  may  happen that the [10X"\r"[110X 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.[133X
  
  [30X    [33X[0;6YThe   function   [2XFFMatOrPermCMtxBinary[102X   ([14X7.3-5[114X)  can  now  read  also
        permutations  stored  in  binary  files  that  have  been created with
        version  2.4 of the C-[5XMeatAxe[105X; note that this format is different from
        the    one    that    is   written   by   version   2.3.   Conversely,
        [2XCMtxBinaryFFMatOrPerm[102X  ([14X7.3-4[114X)  has  been  generalized  such that both
        formats  can  be written. The reference to the C-[5XMeatAxe[105X documentation
        now  points  to  that  of  version  2.4.  Thanks  to Jürgen Müller for
        pointing out this problem.[133X
  
  [30X    [33X[0;6YThe function [2XMeatAxeString[102X ([14X7.3-2[114X) 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-[5XMeatAxe[105X. Thanks to Klaus Lux for pointing out this problem.[133X
  
  [30X    [33X[0;6YDepending  on  the  terminal  capabilities  and  the  user  preference
        [10XDisplayFunction[110X  (see [14X4.2-11[114X), some non-ASCII characters may appear in
        the output shown by [2XDisplayAtlasInfo[102X ([14X3.5-1[114X).[133X
  
  
  [1X1.3-9 [33X[0;0YWhat's New in Version 1.5? (July 2011)[133X[101X
  
  [30X    [33X[0;6YThe function [2XAtlasSubgroup[102X ([14X3.5-9[114X) now admits also the return value of
        [2XOneAtlasGeneratingSetInfo[102X  ([14X3.5-6[114X)  or  the return value of [2XAtlasGroup[102X
        ([14X3.5-8[114X)  as  its first argument. The latter is implemented via the new
        attribute  [2XAtlasRepInfoRecord[102X  ([14X3.5-10[114X),  which  is  set in the groups
        constructed by [2XAtlasGroup[102X ([14X3.5-8[114X).[133X
  
  [30X    [33X[0;6YInformation   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
        [2XOneAtlasGeneratingSetInfo[102X ([14X3.5-6[114X), it is part of the overview shown by
        [2XDisplayAtlasInfo[102X ([14X3.5-1[114X), and it is shown also in the data overview in
        the web, see Section [14X4.3[114X.[133X
  
        [33X[0;6YTwo  new  manual sections about point stabilizers have been added, see
        the sections [14X2.4-6[114X and [14X2.4-7[114X.[133X
  
  [30X    [33X[0;6YInformation   about   the  characters  afforded  by  many  matrix  and
        permutation  representations is now available. If applicable then this
        information     appears     in     the     records     returned     by
        [2XOneAtlasGeneratingSetInfo[102X  ([14X3.5-6[114X),  for  matrix representations it is
        part  of  the  overview  shown  by [2XDisplayAtlasInfo[102X ([14X3.5-1[114X), and it is
        shown also in the data overview in the web, see Section [14X4.3[114X.[133X
  
  [30X    [33X[0;6YThe  functions  [2XCharacter[102X  ([14XReference: Character for a character table
        and  a list[114X), [2XIdentifier[102X ([14XReference: Identifier for character tables[114X),
        [2XIsPrimitive[102X   ([14XReference:   IsPrimitive[114X),   [2XIsTransitive[102X   ([14XReference:
        IsTransitive[114X),  [2XTransitivity[102X ([14XReference: Transitivity[114X), and [2XRankAction[102X
        ([14XReference:  RankAction[114X)  are  now  supported  as  input conditions in
        [2XDisplayAtlasInfo[102X ([14X3.5-1[114X) and [2XOneAtlasGeneratingSetInfo[102X ([14X3.5-6[114X).[133X
  
  [30X    [33X[0;6YIt  is  now  possible  to  restrict the data shown by [2XDisplayAtlasInfo[102X
        ([14X3.5-1[114X) or returned by [2XOneAtlasGeneratingSetInfo[102X ([14X3.5-6[114X) to private or
        non-private data.[133X
  
  [30X    [33X[0;6YA  tutorial  for beginners was added to the manual, see Chapter [14X2[114X, and
        the manual was restructured.[133X
  
  [30X    [33X[0;6YIn  the  overview  shown  by  [2XDisplayAtlasInfo[102X ([14X3.5-1[114X) and in the data
        overview  in  the  web  (see  Section [14X4.3[114X), the ordering of groups was
        improved such that, e.g., [10X"A9"[110X precedes [10X"A10"[110X.[133X
  
  [30X    [33X[0;6YThe function [2XAtlasClassNames[102X ([14X3.4-2[114X) now admits also a Brauer table as
        its  argument,  and  works  also  for  character  tables  of  bicyclic
        extensions of simple groups.[133X
  
  [30X    [33X[0;6YThe   group  names  that  are  entered  in  [2XDisplayAtlasInfo[102X  ([14X3.5-1[114X),
        [2XOneAtlasGeneratingSetInfo[102X ([14X3.5-6[114X), etc., are now case insensitive, and
        if  the  package  [5XCTblLib[105X is available then the admissible group names
        for  the  [5XGAP[105X  character table of the group in question can be used in
        these functions.[133X
  
  [30X    [33X[0;6YIn  order  to reduce the number of global variables, several functions
        have  been  turned  into  components  of  the  new global variable [2XAGR[102X
        ([14X7.1-4[114X).  A few of these functions had been documented in the previous
        version,  the  old  values  are  still  available if the package files
        [11Xgap/obsolete.gd[111X  and  [11Xgap/obsolete.gi[111X  have been read. These files are
        read  automatically  if  [5XGAP[105X's  user preference [10X"ReadObsolete"[110X is [9Xtrue[109X
        when the package gets loaded, see [14X'Reference: The gap.ini file'[114X.[133X
  
  [30X    [33X[0;6YA  few  nicer  characters  are  used  by  [2XDisplayAtlasInfo[102X  ([14X3.5-1[114X) if
        [10XGAPInfo.TermEncoding[110X  has  the  value [10X"UTF-8"[110X and if [2XPrint[102X ([14XReference:
        Print[114X) is not the display function to be used, see Section [14X4.2-11[114X.[133X
  
  [30X    [33X[0;6YA  bug in the function [10XReloadAtlasTableOfContents[110X was fixed. Thanks to
        Jack Schmidt for reporting this bug.[133X
  
  
  [1X1.3-10 [33X[0;0YWhat's New in Version 1.4? (June 2008)[133X[101X
  
  [30X    [33X[0;6YIn  addition  to  the group orders that were added in version 1.3 (see
        Section  [14X1.3-12[114X),  also  many  orders  of  maximal  subgroups  are now
        available.  These values occur in the records returned by [2XAtlasProgram[102X
        ([14X3.5-4[114X)  (for  the  case  of  [10X"maxes"[110X  type programs) and of the three
        argument  version of [2XAtlasGenerators[102X ([14X3.5-3[114X); now a [10Xsize[110X component may
        be bound. In these cases, the groups returned by [2XAtlasSubgroup[102X ([14X3.5-9[114X)
        have the [2XSize[102X ([14XReference: Size[114X) attribute set.[133X
  
  [30X    [33X[0;6YThe  information  about the number of maximal subgroups, if available,
        is now used in [2XDisplayAtlasInfo[102X ([14X3.5-1[114X).[133X
  
  [30X    [33X[0;6YIn  many  cases,  straight  line  programs for computing generators of
        maximal  subgroups  of  a group [22XG[122X, say, can in fact be used to compute
        also  generators  of maximal subgroups of downward extensions of [22XG[122X; if
        not  then it may suffice to extend the given straight line programs by
        additional generators.[133X
  
        [33X[0;6YCurrently  this  yields  more  than  [22X200[122X  new possibilities to compute
        maximal  subgroups,  this  means  a  growth  by  about [22X25[122X percent. For
        example,  all  maximal  subgroups  of  [22X12.M_22[122X  and [22X2.Fi_22[122X can now be
        accessed via [2XAtlasGenerators[102X ([14X3.5-3[114X).[133X
  
        [33X[0;6Y(Of  course this extension means only that one can access the straight
        line  programs  in  question  automatically  via the [5XGAP[105X 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.)[133X
  
        [33X[0;6YFor  this  feature,  information  about  the compatibility of standard
        generators of groups and their factor groups was added.[133X
  
  [30X    [33X[0;6YThe  bibliographies  contained  in the [5XATLAS[105X of Finite Groups [CCN+85]
        and  in  the  [5XATLAS[105X of Brauer Characters [JLPW95] are now available as
        HTML    files,    as    BibXMLext   files,   and   within   [5XGAP[105X,   see
        [2XBrowseBibliographySporadicSimple[102X ([14X3.6-2[114X).[133X
  
  [30X    [33X[0;6YIf  the  [5XGAP[105X  package  [5XBrowse[105X  (see  [BL18])  is  loaded  then the new
        functions           [2XBrowseMinimalDegrees[102X          ([14X3.6-1[114X)          and
        [2XBrowseBibliographySporadicSimple[102X    ([14X3.6-2[114X)   are   available;   these
        functions  can  be  called  also  by  choosing  the corresponding menu
        entries    of    the   [5XBrowse[105X   application   [2XBrowseGapData[102X   ([14XBrowse:
        BrowseGapData[114X).[133X
  
  [30X    [33X[0;6YThe  function  [2XAtlasGroup[102X  ([14X3.5-8[114X) now admits also the return value of
        [2XOneAtlasGeneratingSetInfo[102X ([14X3.5-6[114X) as its argument.[133X
  
  
  [1X1.3-11 [33X[0;0YWhat's New in Version 1.3.1? (October 2007)[133X[101X
  
  [33X[0;0YThis  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  [5XGAP[105X package [5XIO[105X [Neu14] is not available, and pathological situations in
  [2XFFMatOrPermCMtxBinary[102X  ([14X7.3-5[114X)  (concerning  extremely  short corrupted data
  files  and  different  byte  orderings  in  binary  files)  are handled more
  carefully.[133X
  
  [33X[0;0YBesides this, the two functions [2XAtlasGroup[102X ([14X3.5-8[114X) and [2XAtlasSubgroup[102X ([14X3.5-9[114X)
  were  introduced,  and  the  extended function [2XQuaternionAlgebra[102X ([14XReference:
  QuaternionAlgebra[114X)  of  [5XGAP[105X 4.4.10 can now be used for describing base rings
  in [2XOneAtlasGeneratingSetInfo[102X ([14X3.5-6[114X) and [2XAllAtlasGeneratingSetInfos[102X ([14X3.5-7[114X).
  (This  is  the  reason  why  this  version  of the package requires at least
  version 4.4.10 of [5XGAP[105X.)[133X
  
  
  [1X1.3-12 [33X[0;0YWhat's New in Version 1.3? (June 2007)[133X[101X
  
  [30X    [33X[0;6YThe  database  was extended, see Section [14X4.2-4[114X for the number and size
        of files.[133X
  
  [30X    [33X[0;6YNew data types and corresponding [5XGAP[105X objects have been introduced, for
        representing   semi-presentations,  presentations,  and  programs  for
        finding  standard  generators.  For details, see [2XAtlasProgram[102X ([14X3.5-4[114X),
        Chapter [14X6[114X, and Section [14X7.6[114X.[133X
  
  [30X    [33X[0;6YThe   records  returned  by  the  functions  [2XAtlasGenerators[102X  ([14X3.5-3[114X),
        [2XOneAtlasGeneratingSetInfo[102X   ([14X3.5-6[114X),   and  [2XAllAtlasGeneratingSetInfos[102X
        ([14X3.5-7[114X)  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.[133X
  
  [30X    [33X[0;6YFor  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  [2XDisplayAtlasInfo[102X  ([14X3.5-1[114X),  [2XOneAtlasGeneratingSetInfo[102X
        ([14X3.5-6[114X), and [2XAllAtlasGeneratingSetInfos[102X ([14X3.5-7[114X), see also Section [14X6.3[114X.
        For  these  functions,  also properties such as [2XIsPrimeInt[102X ([14XReference:
        IsPrimeInt[114X)  can  be  used to describe the intended restriction of the
        output.[133X
  
  [30X    [33X[0;6YOne   can   now   use   [2XPager[102X   ([14XReference:  Pager[114X)  functionality  in
        [2XDisplayAtlasInfo[102X ([14X3.5-1[114X), see Section [14X4.2-11[114X.[133X
  
        [33X[0;6YAn  interactive alternative to [2XDisplayAtlasInfo[102X ([14X3.5-1[114X) is provided by
        the  function  [2XBrowseAtlasInfo[102X  ([14XBrowse: BrowseAtlasInfo[114X) from the new
        (recommended) [5XGAP[105X package [5XBrowse[105X (see [BL18]).[133X
  
  [30X    [33X[0;6YThe      functions      [2XOneAtlasGeneratingSetInfo[102X      ([14X3.5-6[114X)     and
        [2XAllAtlasGeneratingSetInfos[102X  ([14X3.5-7[114X)  now  admit  also  a list of group
        names as the first argument.[133X
  
  [30X    [33X[0;6YThe  functions  for actually accessing the data are more flexible now,
        see Section [14X7.2[114X.[133X
  
  [30X    [33X[0;6YFor transferring remote data, the [5XGAP[105X package [5XIO[105X (see [Neu14]) can now
        be used (and is recommended) as an alternative to [11Xwget[111X.[133X
  
  [30X    [33X[0;6YThe  address  of the data server has changed. The access to the server
        is  no  longer possible via [11Xftp[111X, thus the mechanism used up to version
        1.2, which was based on [11Xftp[111X, had to be rewritten.[133X
  
        [33X[0;6YThe  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 [13Xcompute[113X the
        table of contents directly from the server data, but on the other hand
        the  update  information  can  be  [13Xdownloaded[113X without the necessity to
        install [11Xperl[111X.[133X
  
        [33X[0;6YAnother consequence is that the system program [11Xls[111X is no longer needed,
        see Section [14X1.3-14[114X.[133X
  
  [30X    [33X[0;6YThe package manual has been restructured, extended and improved. It is
        now based on the package [5XGAPDoc[105X (see [LN18]).[133X
  
  
  [1X1.3-13 [33X[0;0YWhat's New in Version 1.2? (November 2003)[133X[101X
  
  [33X[0;0YNot much.[133X
  
  [33X[0;0YThe release of Version 1.2 became necessary first of all in order to provide
  a   package   version   that   is   compatible   with  [5XGAP[105X 4.4,  since  some
  cross-references into the [5XGAP[105X 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.[133X
  
  [33X[0;0YThis opportunity was used[133X
  
  [30X    [33X[0;6Yto  upgrade  the  administrational part for loading the package to the
        mechanism that is recommended for [5XGAP[105X 4.4,[133X
  
  [30X    [33X[0;6Yto  extend  the  test  suite, which now covers more consistency checks
        using the [5XGAP[105X Character Table Library (see [Bre22]),[133X
  
  [30X    [33X[0;6Yto  make  the function [2XScanMeatAxeFile[102X ([14X7.3-1[114X) more robust, due to the
        fact  that the [5XGAP[105X function [2XPermList[102X ([14XReference: PermList[114X) now returns
        [9Xfail[109X instead of raising an error,[133X
  
  [30X    [33X[0;6Yto  change  the way how representations with prescribed properties are
        accessed  (the  new  function [2XOneAtlasGeneratingSetInfo[102X ([14X3.5-6[114X) is now
        preferred     to     the     former     [10XOneAtlasGeneratingSet[110X,     and
        [2XAllAtlasGeneratingSetInfos[102X  ([14X3.5-7[114X) has been added in order to provide
        programmatic  access  in  parallel  to the human readable descriptions
        printed by [2XDisplayAtlasInfo[102X ([14X3.5-1[114X)),[133X
  
  [30X    [33X[0;6Yand last but not least to include the current table of contents of the
        underlying database.[133X
  
  [33X[0;0YFor  [5XAtlasRep[105X  users, the new feature of [5XGAP[105X 4.4 is particularly interesting
  that due to better kernel support, reading large matrices over finite fields
  is now faster than it was in [5XGAP[105X 4.3.[133X
  
  
  [1X1.3-14 [33X[0;0YWhat's New in Version 1.1? (October 2002)[133X[101X
  
  [33X[0;0YThe   biggest   change  w. r. t. Version 1.1  is  the  addition  of  private
  extensions  (see Chapter [14X5[114X). It includes a new [21Xfree format[121X for straight line
  programs  (see Section [14X5.2[114X). Unfortunately, this feature requires the system
  program  [11Xls[111X,  so  it  may  be  not  available  for  example under MS Windows
  operating systems. [But see Section [14X1.3-12[114X.][133X
  
  [33X[0;0YIn order to admit the addition of other types of data, the implementation of
  several functions has been changed. Data types are described in Section [14X7.5[114X.
  An  example  of  a  new  data  type  are  quaternionic  representations (see
  Section [14X7.6[114X). The user interface itself (see Chapter [14X3[114X) remained the same.[133X
  
  [33X[0;0YAs  an alternative to [10Xperl[110X, one can use [10Xwget[110X now for transferring data files
  (see [14X4.2[114X).[133X
  
  [33X[0;0YData  files can be read much more efficiently in [5XGAP[105X 4.3 than in [5XGAP[105X 4.2. In
  Version 1.1  of  the  [5XAtlasRep[105X  package,  this  feature  is used for reading
  matrices  and  permutations  in  [5XMeatAxe[105X  text  format  with [2XScanMeatAxeFile[102X
  ([14X7.3-1[114X).  As  a  consequence,  (at  least)  [5XGAP[105X 4.3 is required for [5XAtlasRep[105X
  Version 1.1.[133X
  
  [33X[0;0YThe     new     [10Xcompress[110X     component     of     the     global    variable
  [2XAtlasOfGroupRepresentationsInfo[102X  ([14X7.1-5[114X)  allows  one  to  store  data files
  automatically in [11Xgzip[111Xped form.[133X
  
  [33X[0;0YFor  matrix  representations  in  characteristic  zero,  invariant forms and
  generators for the centralizer algebra are now accessible in [5XGAP[105X if they are
  contained  in  the  source  files  –this  information  had  been  ignored in
  Version 1.0.[133X
  
  [33X[0;0YAdditional information is now available via the internet (see [14X4.3[114X).[133X
  
  [33X[0;0YThe facilities for updating the table of contents have been extended.[133X
  
  [33X[0;0YThe  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.[133X
  
  [33X[0;0YApart  from these changes, a few minor bugs in the handling of [5XMeatAxe[105X files
  have  been  fixed,  typos  in the documentation have been corrected, and the
  syntax checks for [5XATLAS[105X straight line programs (see [14X7.4[114X) have been improved.[133X
  
  
  [1X1.4 [33X[0;0YAcknowledgements[133X[101X
  
  [30X    [33X[0;6YFrank  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
        [21Xstandard[121X perl.[133X
  
  [30X    [33X[0;6YUlrich Kaiser helped with preparing the package for MS Windows.[133X
  
  [30X    [33X[0;6YKlaus  Lux  had the idea to support data extensions, see Chapter [14X5[114X, he
        did a lot of beta testing, and helped to fix several bugs.[133X
  
  [30X    [33X[0;6YFrank  Lübeck  contributed the functions [2XCMtxBinaryFFMatOrPerm[102X ([14X7.3-4[114X)
        and [2XFFMatOrPermCMtxBinary[102X ([14X7.3-5[114X).[133X
  
  [30X    [33X[0;6YFrank Lübeck and Max Neunhöffer wrote the [5XGAPDoc[105X package [LN18], which
        is  used  for processing the documentation of the [5XAtlasRep[105X package and
        for  processing  the  bibliographies  included  in  this  package (see
        [2XBrowseBibliographySporadicSimple[102X ([14X3.6-2[114X)),[133X
  
  [30X    [33X[0;6YMax  Neunhöffer wrote the [5XGAP[105X package [5XIO[105X [Neu14], which is recommended
        for transferring data.[133X
  
  [30X    [33X[0;6YMax  Neunhöffer  has  also  suggested  the  generalization of the data
        access  described  in  Section [14X7.2[114X,  the admissibility of the function
        [2XCharacter[102X ([14XReference: Character for a character table and a list[114X) as a
        filter in [2XDisplayAtlasInfo[102X ([14X3.5-1[114X), [2XOneAtlasGeneratingSetInfo[102X ([14X3.5-6[114X),
        and   [2XAllAtlasGeneratingSetInfos[102X   ([14X3.5-7[114X),   and   the   variant   of
        [2XAtlasRepInfoRecord[102X ([14X3.5-10[114X) that takes a group name as its input.[133X
  
  [30X    [33X[0;6YGunter  Malle  suggested to make the information about representations
        of minimal degree accessible, see Section [14X6.3[114X.[133X
  
  [30X    [33X[0;6YAndries Brouwer suggested to add a tutorial (see Chapter [14X2[114X), Klaus Lux
        suggested several improvements of this chapter.[133X
  
  [30X    [33X[0;6YThe  development of this [5XGAP[105X package has been supported by the SFB-TRR
        195   [21XSymbolic   Tools   in   Mathematics   and   their   Applications[121X
        ([7Xhttps://www.computeralgebra.de/sfb/[107X) (from 2017 until 2022).[133X
  
