  
  [1X3 [33X[0;0YThe User Interface of the [5XAtlasRep[105X[101X[1X Package[133X[101X
  
  [33X[0;0YThe  [13Xuser  interface[113X  is  the  part  of the [5XGAP[105X interface that allows one to
  display information about the current contents of the database and to access
  individual  data  (perhaps  by  downloading  them,  see  Section [14X4.2-1[114X). The
  corresponding  functions  are described in this chapter. See Section [14X2.4[114X for
  some small examples how to use the functions of the interface.[133X
  
  [33X[0;0YData  extensions of the [5XAtlasRep[105X package are regarded as another part of the
  [5XGAP[105X  interface, they are described in Chapter [14X5[114X. Finally, the low level part
  of the interface is described in Chapter [14X7[114X.[133X
  
  
  [1X3.1 [33X[0;0YDownloading [5XAtlasRep[105X[101X[1X Data[133X[101X
  
  [33X[0;0YThose  functions  from  the  package that access data from the web [5XATLAS[105X may
  have  to  download  these  data if they are not (yet) stored locally. It may
  happen  that  downloads are not successful, for example if one is offline or
  if  the remote data are temporarily not reachable. In these cases, functions
  such as [2XAtlasGroup[102X ([14X3.6-8[114X) return [9Xfail[109X.[133X
  
  [33X[0;0YIn  order  to inspect the reason for a failed download, one can set the info
  level of [2XInfoAtlasRep[102X ([14X7.1-1[114X) to at least [10X2[110X and try again.[133X
  
  [33X[0;0YIt  may  make  sense  to  restrict the time for downloads, using the [21Xtimeout[121X
  feature  of  [2XDownload[102X  ([14XUtils:  Download[114X).  An upper bound for the number of
  seconds which may be spent on the download of a file can be set globally via
  the   user   preference   [10XDownloadMaxTime[110X   (see   [14X'Utils:  User  preference
  DownloadMaxTime'[114X)  of  the  [5Xutils[105X  package. The default is the value [10X0[110X which
  means  that  there  is  no  upper bound. For individual function calls, this
  preference can be overwritten via the global option [10XmaxTime[110X, where the value
  is  again  the maximal number of seconds. The following example is realistic
  if  the  data  in  question  are not yet stored locally and if your internet
  connection is not very fast.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XAtlasGroup( "B", Characteristic, 5 : maxTime:= 1 );[127X[104X
    [4X[28Xfail[128X[104X
    [4X[25Xgap>[125X [27XAtlasGroup( "B", Characteristic, 5 : maxTime:= 5 );[127X[104X
    [4X[28X<matrix group of size 4154781481226426191177580544000000 with 2 generators>[128X[104X
  [4X[32X[104X
  
  
  [1X3.2 [33X[0;0YAccessing vs. Constructing Representations[133X[101X
  
  [33X[0;0YNote  that  [13Xaccessing[113X the data means in particular that it is [13Xnot[113X the aim of
  this  package  to [13Xconstruct[113X representations from known ones. For example, if
  at  least  one  permutation  representation  for  a group [22XG[122X is stored but no
  matrix   representation   in   a   positive   characteristic  [22Xp[122X,  say,  then
  [2XOneAtlasGeneratingSetInfo[102X  ([14X3.6-6[114X)  returns  [9Xfail[109X  when  it  is  asked for a
  description of an available set of matrix generators for [22XG[122X in characteristic
  [22Xp[122X,  although  such a representation can be obtained by reduction modulo [22Xp[122X of
  an integral matrix representation, which in turn can be constructed from any
  permutation representation.[133X
  
  
  [1X3.3 [33X[0;0YGroup Names Used in the [5XAtlasRep[105X[101X[1X Package[133X[101X
  
  [33X[0;0YWhen  you  access  data  via  the [5XAtlasRep[105X package, you specify the group in
  question  by  an  admissible [13Xname[113X. Thus it is essential to know these names,
  which are called [13Xthe [5XGAP[105X names[113X of the group in the following.[133X
  
  [33X[0;0YFor  a  group  [22XG[122X, say, whose character table is available in [5XGAP[105X's Character
  Table  Library  (see  [Bre25]), the admissible names of [22XG[122X are the admissible
  names  of  this character table. One such name is the [2XIdentifier[102X ([14XReference:
  Identifier for character tables[114X) value of the character table, see [14X'CTblLib:
  Admissible Names for Character Tables in CTblLib'[114X. This name is usually very
  similar  to  the  name  used  in  the  [5XATLAS[105X  of Finite Groups [CCN+85]. For
  example,  [10X"M22"[110X is a [5XGAP[105X name of the Mathieu group [22XM_22[122X, [10X"12_1.U4(3).2_1"[110X is
  a  [5XGAP[105X  name of [22X12_1.U_4(3).2_1[122X, the two names [10X"S5"[110X and [10X"A5.2"[110X are [5XGAP[105X names
  of  the  symmetric  group  [22XS_5[122X,  and the two names [10X"F3+"[110X and [10X"Fi24'"[110X are [5XGAP[105X
  names of the simple Fischer group [22XFi_24^'[122X.[133X
  
  [33X[0;0YWhen a [5XGAP[105X name is required as an input of a package function, this input is
  case  insensitive.  For  example,  both [10X"A5"[110X and [10X"a5"[110X are valid arguments of
  [2XDisplayAtlasInfo[102X ([14X3.6-1[114X).[133X
  
  [33X[0;0YInternally,  for example as part of filenames (see Section [14X7.6[114X), the package
  uses  names  that  may  differ  from  the  [5XGAP[105X names; these names are called
  [13X[5XATLAS[105X-file names[113X. For example, [10X"A5"[110X, [10X"TE62"[110X, and [10X"F24"[110X are [5XATLAS[105X-file names.
  Of  these,  only  [10X"A5"[110X  is  also  a  [5XGAP[105X  name,  but  the other two are not;
  corresponding [5XGAP[105X names are [10X"2E6(2)"[110X and [10X"Fi24'"[110X, respectively.[133X
  
  
  [1X3.4 [33X[0;0YStandard Generators Used in the [5XAtlasRep[105X[101X[1X Package[133X[101X
  
  [33X[0;0YFor the general definition of [13Xstandard generators[113X of a group, see [Wil96].[133X
  
  [33X[0;0YSeveral  [13Xdifferent[113X  standard  generators  may  be  defined  for a group, the
  definitions for each group that occurs in the [5XATLAS[105X of Group Representations
  can be found at[133X
  
  [33X[0;0Y[7Xhttp://atlas.math.rwth-aachen.de/Atlas/v3[107X.[133X
  
  [33X[0;0YWhen  one specifies the standardization, the [22Xi[122X-th set of standard generators
  is  denoted  by  the  number [22Xi[122X. Note that when more than one set of standard
  generators  is  defined  for  a group, one must be careful to use [13Xcompatible
  standardization[113X.  For  example,  the  straight  line programs, straight line
  decisions  and  black  box  programs  in  the  database  refer to a specific
  standardization  of  their  inputs.  That  is,  a  straight line program for
  computing  generators of a certain subgroup of a group [22XG[122X is defined only for
  a  specific  set  of  standard  generators of [22XG[122X, and applying the program to
  matrix   or   permutation   generators   of   [22XG[122X   but  w. r. t. a  different
  standardization  may  yield  unpredictable  results.  Therefore  the results
  returned  by  the  functions  described  in this chapter contain information
  about the standardizations they refer to.[133X
  
  
  [1X3.5 [33X[0;0YClass Names Used in the [5XAtlasRep[105X[101X[1X Package[133X[101X
  
  [33X[0;0YFor  each  straight  line program (see [2XAtlasProgram[102X ([14X3.6-4[114X)) that is used to
  compute  lists  of  class  representatives,  it is essential to describe the
  classes  in  which these elements lie. Therefore, in these cases the records
  returned  by  the  function [2XAtlasProgram[102X ([14X3.6-4[114X) contain a component [10Xoutputs[110X
  with value a list of [13Xclass names[113X.[133X
  
  [33X[0;0YCurrently  we  define  these  class names only for simple groups and certain
  extensions of simple groups, see Section [14X3.5-1[114X. The function [2XAtlasClassNames[102X
  ([14X3.5-2[114X)  can  be  used to compute the list of class names from the character
  table in the [5XGAP[105X Library.[133X
  
  
  [1X3.5-1 [33X[0;0YDefinition of [5XATLAS[105X[101X[1X Class Names[133X[101X
  
  [33X[0;0YFor  the definition of class names of an almost simple group, we assume that
  the  ordinary  character tables of all nontrivial normal subgroups are shown
  in the [5XATLAS[105X of Finite Groups [CCN+85].[133X
  
  [33X[0;0YEach  class name is a string consisting of the element order of the class in
  question  followed  by  a  combination  of  capital letters, digits, and the
  characters  [10X'[110X and [10X-[110X (starting with a capital letter). For example, [10X1A[110X, [10X12A1[110X,
  and  [10X3B'[110X  denote  the  class  that contains the identity element, a class of
  element order [22X12[122X, and a class of element order [22X3[122X, respectively.[133X
  
  [31X1[131X   [33X[0;6YFor  the  table  of  a  [13Xsimple[113X  group, the class names are the same as
        returned  by  the  two argument version of the [5XGAP[105X function [2XClassNames[102X
        ([14XReference:  ClassNames[114X),  cf. [CCN+85,  Chapter  7,  Section  5]: The
        classes  are  arranged  w. r. t. increasing element order and for each
        element  order  w. r. t. decreasing  centralizer  order, the conjugacy
        classes  that  contain  elements of order [22Xn[122X are named [22Xn[122X[10XA[110X, [22Xn[122X[10XB[110X, [22Xn[122X[10XC[110X, [22X...[122X;
        the  alphabet  used  here  is potentially infinite, and reads [10XA[110X, [10XB[110X, [10XC[110X,
        [22X...[122X, [10XZ[110X, [10XA1[110X, [10XB1[110X, [22X...[122X, [10XA2[110X, [10XB2[110X, [22X...[122X.[133X
  
        [33X[0;6YFor  example,  the classes of the alternating group [22XA_5[122X have the names
        [10X1A[110X, [10X2A[110X, [10X3A[110X, [10X5A[110X, and [10X5B[110X.[133X
  
  [31X2[131X   [33X[0;6YNext we consider the case of an [13Xupward extension[113X [22XG.A[122X of a simple group
        [22XG[122X by a [13Xcyclic[113X group of order [22XA[122X. The [5XATLAS[105X defines class names for each
        element  [22Xg[122X  of [22XG.A[122X only w. r. t. the group [22XG.a[122X, say, that is generated
        by  [22XG[122X  and [22Xg[122X; namely, there is a power of [22Xg[122X (with the exponent coprime
        to  the order of [22Xg[122X) for which the class has a name of the same form as
        the  class  names  for  simple  groups, and the name of the class of [22Xg[122X
        w. r. t. [22XG.a[122X  is  then obtained from this name by appending a suitable
        number  of  dashes [10X'[110X.  So  dashed  class  names refer exactly to those
        classes that are not printed in the [5XATLAS[105X.[133X
  
        [33X[0;6YFor  example, those classes of the symmetric group [22XS_5[122X that do not lie
        in  [22XA_5[122X  have the names [10X2B[110X, [10X4A[110X, and [10X6A[110X. The outer classes of the group
        [22XL_2(8).3[122X  have  the  names  [10X3B[110X,  [10X6A[110X,  [10X9D[110X, and [10X3B'[110X, [10X6A'[110X, [10X9D'[110X. The outer
        elements  of  order  [22X5[122X  in  the group [22XSz(32).5[122X lie in the classes with
        names [10X5B[110X, [10X5B'[110X, [10X5B''[110X, and [10X5B'''[110X.[133X
  
        [33X[0;6YIn the group [22XG.A[122X, the class of [22Xg[122X may fuse with other classes. The name
        of  the  class  of [22Xg[122X in [22XG.A[122X is obtained from the names of the involved
        classes of [22XG.a[122X by concatenating their names after removing the element
        order part from all of them except the first one.[133X
  
        [33X[0;6YFor  example,  the  elements  of  order  [22X9[122X  in the group [22XL_2(27).6[122X are
        contained  in the subgroup [22XL_2(27).3[122X but not in [22XL_2(27)[122X. In [22XL_2(27).3[122X,
        they  lie  in  the  classes  [10X9A[110X, [10X9A'[110X, [10X9B[110X, and [10X9B'[110X; in [22XL_2(27).6[122X, these
        classes fuse to [10X9AB[110X and [10X9A'B'[110X.[133X
  
  [31X3[131X   [33X[0;6YNow  we  define  class  names  for  [13Xgeneral upward extensions[113X [22XG.A[122X of a
        simple  group  [22XG[122X.  Each  element  [22Xg[122X  of such a group lies in an upward
        extension  [22XG.a[122X by a cyclic group, and the class names w. r. t. [22XG.a[122X are
        already  defined.  The  name  of  the class of [22Xg[122X in [22XG.A[122X is obtained by
        concatenating  the  names  of  the  classes in the orbit of [22XG.A[122X on the
        classes  of  cyclic  upward  extensions of [22XG[122X, after ordering the names
        lexicographically and removing the element order part from all of them
        except  the  first one. An [13Xexception[113X is the situation where dashed and
        non-dashed  class  names  appear in an orbit; in this case, the dashed
        names are omitted.[133X
  
        [33X[0;6YFor  example,  the  classes  [10X21A[110X and [10X21B[110X of the group [22XU_3(5).3[122X fuse in
        [22XU_3(5).S_3[122X  to the class [10X21AB[110X, and the class [10X2B[110X of [22XU_3(5).2[122X fuses with
        the  involution  classes  [10X2B'[110X,  [10X2B''[110X  in  the  groups  [22XU_3(5).2^'[122X  and
        [22XU_3(5).2^{''}[122X to the class [10X2B[110X of [22XU_3(5).S_3[122X.[133X
  
        [33X[0;6YIt  may  happen  that  some names in the [10Xoutputs[110X component of a record
        returned by [2XAtlasProgram[102X ([14X3.6-4[114X) do not uniquely determine the classes
        of   the  corresponding  elements.  For  example,  the  (algebraically
        conjugate)  classes  [10X39A[110X  and  [10X39B[110X  of  the  group  [22XCo_1[122X have not been
        distinguished  yet. In such cases, the names used contain a minus sign
        [10X-[110X,  and  mean  [21Xone  of  the classes in the range described by the name
        before  and  the  name after the minus sign[121X; the element order part of
        the  name  does not appear after the minus sign. So the name [10X39A-B[110X for
        the  group  [22XCo_1[122X means [10X39A[110X or [10X39B[110X, and the name [10X20A-B'''[110X for the group
        [22XSz(32).5[122X  means  one  of the classes of element order [22X20[122X in this group
        (these classes lie outside the simple group [22XSz[122X).[133X
  
  [31X4[131X   [33X[0;6YFor  a  [13Xdownward  extension[113X  [22Xm.G.A[122X  of an almost simple group [22XG.A[122X by a
        cyclic  group  of  order  [22Xm[122X, let [22Xπ[122X denote the natural epimorphism from
        [22Xm.G.A[122X onto [22XG.A[122X. Each class name of [22Xm.G.A[122X has the form [10XnX_0[110X, [10XnX_1[110X etc.,
        where  [10XnX[110X is the class name of the image under [22Xπ[122X, and the indices [10X0[110X, [10X1[110X
        etc.  are chosen according to the position of the class in the lifting
        order  rows  for [22XG[122X, see [CCN+85, Chapter 7, Section 7, and the example
        in Section 8]).[133X
  
        [33X[0;6YFor example, if [22Xm = 6[122X then [10X1A_1[110X and [10X1A_5[110X denote the classes containing
        the  generators of the kernel of [22Xπ[122X, that is, central elements of order
        [22X6[122X.[133X
  
  [1X3.5-2 AtlasClassNames[101X
  
  [33X[1;0Y[29X[2XAtlasClassNames[102X( [3Xtbl[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Ya list of class names.[133X
  
  [33X[0;0YLet  [3Xtbl[103X  be the ordinary or modular character table of a group [22XG[122X, say, that
  is  almost simple or a downward extension of an almost simple group and such
  that  [3Xtbl[103X  is an [5XATLAS[105X table from the [5XGAP[105X Character Table Library, according
  to  its  [2XInfoText[102X  ([14XReference: InfoText[114X) value. Then [2XAtlasClassNames[102X returns
  the  list of class names for [22XG[122X, as defined in Section [14X3.5-1[114X. The ordering of
  class names is the same as the ordering of the columns of [3Xtbl[103X.[133X
  
  [33X[0;0Y(The  function may work also for character tables that are not [5XATLAS[105X tables,
  but then clearly the class names returned are somewhat arbitrary.)[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XAtlasClassNames( CharacterTable( "L3(4).3" ) );[127X[104X
    [4X[28X[ "1A", "2A", "3A", "4ABC", "5A", "5B", "7A", "7B", "3B", "3B'", [128X[104X
    [4X[28X  "3C", "3C'", "6B", "6B'", "15A", "15A'", "15B", "15B'", "21A", [128X[104X
    [4X[28X  "21A'", "21B", "21B'" ][128X[104X
    [4X[25Xgap>[125X [27XAtlasClassNames( CharacterTable( "U3(5).2" ) );[127X[104X
    [4X[28X[ "1A", "2A", "3A", "4A", "5A", "5B", "5CD", "6A", "7AB", "8AB", [128X[104X
    [4X[28X  "10A", "2B", "4B", "6D", "8C", "10B", "12B", "20A", "20B" ][128X[104X
    [4X[25Xgap>[125X [27XAtlasClassNames( CharacterTable( "L2(27).6" ) );[127X[104X
    [4X[28X[ "1A", "2A", "3AB", "7ABC", "13ABC", "13DEF", "14ABC", "2B", "4A", [128X[104X
    [4X[28X  "26ABC", "26DEF", "28ABC", "28DEF", "3C", "3C'", "6A", "6A'", [128X[104X
    [4X[28X  "9AB", "9A'B'", "6B", "6B'", "12A", "12A'" ][128X[104X
    [4X[25Xgap>[125X [27XAtlasClassNames( CharacterTable( "L3(4).3.2_2" ) );[127X[104X
    [4X[28X[ "1A", "2A", "3A", "4ABC", "5AB", "7A", "7B", "3B", "3C", "6B", [128X[104X
    [4X[28X  "15A", "15B", "21A", "21B", "2C", "4E", "6E", "8D", "14A", "14B" ][128X[104X
    [4X[25Xgap>[125X [27XAtlasClassNames( CharacterTable( "3.A6" ) );[127X[104X
    [4X[28X[ "1A_0", "1A_1", "1A_2", "2A_0", "2A_1", "2A_2", "3A_0", "3B_0", [128X[104X
    [4X[28X  "4A_0", "4A_1", "4A_2", "5A_0", "5A_1", "5A_2", "5B_0", "5B_1", [128X[104X
    [4X[28X  "5B_2" ][128X[104X
    [4X[25Xgap>[125X [27XAtlasClassNames( CharacterTable( "2.A5.2" ) );[127X[104X
    [4X[28X[ "1A_0", "1A_1", "2A_0", "3A_0", "3A_1", "5AB_0", "5AB_1", "2B_0", [128X[104X
    [4X[28X  "4A_0", "4A_1", "6A_0", "6A_1" ][128X[104X
  [4X[32X[104X
  
  [1X3.5-3 AtlasCharacterNames[101X
  
  [33X[1;0Y[29X[2XAtlasCharacterNames[102X( [3Xtbl[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Ya list of character names.[133X
  
  [33X[0;0YLet  [3Xtbl[103X  be  the  ordinary  or  modular  character table of a simple group.
  [2XAtlasCharacterNames[102X returns a list of strings, the [22Xi[122X-th entry being the name
  of  the  [22Xi[122X-th irreducible character of [3Xtbl[103X; this name consists of the degree
  of this character followed by distinguishing lowercase letters.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XAtlasCharacterNames( CharacterTable( "A5" ) );                   [127X[104X
    [4X[28X[ "1a", "3a", "3b", "4a", "5a" ][128X[104X
  [4X[32X[104X
  
  
  [1X3.6 [33X[0;0YAccessing Data via [5XAtlasRep[105X[101X[1X[133X[101X
  
  [33X[0;0YThe examples shown in this section refer to the situation that no extensions
  have  been  notified,  and to a perhaps outdated table of contents. That is,
  the  current  version  of  the database may contain more information than is
  shown here.[133X
  
  [1X3.6-1 DisplayAtlasInfo[101X
  
  [33X[1;0Y[29X[2XDisplayAtlasInfo[102X( [[3Xlistofnames[103X][,] [[3Xstd[103X][,] [[3X"contents"[103X, [3Xsources[103X][,] [[3X...[103X] ) [32X function[133X
  [33X[1;0Y[29X[2XDisplayAtlasInfo[102X( [3Xgapname[103X[, [3Xstd[103X][, [3X...[103X] ) [32X function[133X
  
  [33X[0;0YThis  function lists the information available via the [5XAtlasRep[105X package, for
  the given input.[133X
  
  [33X[0;0YThere are essentially three ways of calling this function.[133X
  
  [30X    [33X[0;6YIf there is no argument or if the first argument is a list [3Xlistofnames[103X
        of  strings  that  are  [5XGAP[105X names of groups, [2XDisplayAtlasInfo[102X shows an
        overview of the known information.[133X
  
  [30X    [33X[0;6YIf  the  first  argument  is  a string [3Xgapname[103X that is a [5XGAP[105X name of a
        group,  [2XDisplayAtlasInfo[102X  shows an overview of the information that is
        available for this group.[133X
  
  [30X    [33X[0;6YIf  the string [10X"contents"[110X is the only argument then the function shows
        which  parts  of  the  database  are available; these are at least the
        [10X"core"[110X   part,   which   means  the  data  from  the  [5XATLAS[105X  of  Group
        Representations,  and  the  [10X"internal"[110X part, which means the data that
        are  distributed  with  the  [5XAtlasRep[105X  package. Other parts can become
        available  by  calls to [2XAtlasOfGroupRepresentationsNotifyData[102X ([14X5.1-1[114X).
        Note  that the shown numbers of locally available files depend on what
        has already been downloaded.[133X
  
  [33X[0;0YIn  each  case, the information will be printed to the screen or will be fed
  into   a   pager,   see   Section  [14X4.2-11[114X.  An  interactive  alternative  to
  [2XDisplayAtlasInfo[102X  is the function [2XBrowseAtlasInfo[102X ([14XBrowse: BrowseAtlasInfo[114X),
  see [BL26].[133X
  
  [33X[0;0YThe  following  paragraphs  describe  the structure of the output in the two
  cases. Examples can be found in Section [14X3.6-2[114X.[133X
  
  [33X[0;0YCalled  without arguments, [2XDisplayAtlasInfo[102X shows a general overview for all
  groups. If some information is available for the group [22XG[122X, say, then one line
  is shown for [22XG[122X, with the following columns.[133X
  
  [8X[10Xgroup[110X[8X[108X
        [33X[0;6Ythe  [5XGAP[105X  name  of  [22XG[122X  (see  Section [14X3.3[114X), if applicable followed by a
        string  (by  default  a  star  [10X*[110X)  indicating that at least one column
        refers  to  data  not  belonging to the core part of the database (see
        Section [14X4.2-12[114X).[133X
  
  [8X[10X#[110X[8X[108X
        [33X[0;6Ythe  number  of faithful representations stored for [22XG[122X that satisfy the
        additional conditions given (see below),[133X
  
  [8X[10Xmaxes[110X[8X[108X
        [33X[0;6Ythe   number   of  available  straight  line  programs  for  computing
        generators of maximal subgroups of [22XG[122X,[133X
  
  [8X[10Xcl[110X[8X[108X
        [33X[0;6Ya  [10X+[110X  sign  if  at  least one program for computing representatives of
        conjugacy classes of elements of [22XG[122X is stored,[133X
  
  [8X[10Xcyc[110X[8X[108X
        [33X[0;6Ya  [10X+[110X  sign  if  at  least one program for computing representatives of
        classes of maximally cyclic subgroups of [22XG[122X is stored,[133X
  
  [8X[10Xout[110X[8X[108X
        [33X[0;6Ydescriptions  of  outer  automorphisms  of  [22XG[122X  for  which at least one
        program is stored,[133X
  
  [8X[10Xfnd[110X[8X[108X
        [33X[0;6Ya  [10X+[110X  sign  if  at least one program is available for finding standard
        generators,[133X
  
  [8X[10Xchk[110X[8X[108X
        [33X[0;6Ya  [10X+[110X  sign if at least one program is available for checking whether a
        set of generators is a set of standard generators, and[133X
  
  [8X[10Xprs[110X[8X[108X
        [33X[0;6Ya  [10X+[110X  sign  if  at  least  one  program  is  available  that encodes a
        presentation.[133X
  
  [33X[0;0YCalled with a list [3Xlistofnames[103X of strings that are [5XGAP[105X names of some groups,
  [2XDisplayAtlasInfo[102X  prints  the overview described above but restricted to the
  groups in this list.[133X
  
  [33X[0;0YIn  addition  to  or  instead  of  [3Xlistofnames[103X,  the string [10X"contents"[110X and a
  description  [22Xsources[122X  of  the  data may be given about which the overview is
  formed. See below for admissible values of [22Xsources[122X.[133X
  
  [33X[0;0YCalled with a string [3Xgapname[103X that is a [5XGAP[105X name of a group, [2XDisplayAtlasInfo[102X
  prints  an overview of the information that is available for this group. One
  line is printed for each faithful representation, showing the number of this
  representation  (which can be used in calls of [2XAtlasGenerators[102X ([14X3.6-3[114X)), and
  a  string  of  one  of the following forms; in both cases, [22Xid[122X is a (possibly
  empty) string.[133X
  
  [8X[10XG <= Sym([110X[8X[22Xn[122X[22Xid[122X[10X)[110X[8X[108X
        [33X[0;6Ydenotes  a  permutation  representation  of degree [22Xn[122X, for example [10XG <=
        Sym(40a)[110X  and [10XG <= Sym(40b)[110X denote two (nonequivalent) representations
        of degree [22X40[122X.[133X
  
  [8X[10XG <= GL([110X[8X[22Xn[122X[22Xid[122X,[22Xdescr[122X[10X)[110X[8X[108X
        [33X[0;6Ydenotes a matrix representation of dimension [22Xn[122X over a coefficient ring
        described  by  [22Xdescr[122X, which can be a prime power, [10Xℤ[110X (denoting the ring
        of  integers),  a  description  of  an  algebraic  extension  field, [10Xℂ[110X
        (denoting  an  unspecified  algebraic extension field), or [10Xℤ/[110X[22Xm[122X[10Xℤ[110X for an
        integer  [22Xm[122X  (denoting  the  ring of residues mod [22Xm[122X); for example, [10XG <=
        GL(2a,4)[110X  and [10XG <= GL(2b,4)[110X denote two (nonequivalent) representations
        of dimension [22X2[122X over the field with four elements.[133X
  
  [33X[0;0YBelow the representations, the programs available for [3Xgapname[103X are listed. In
  each  row  of  the  overview, the entry in the first column is followed by a
  string  (by default a star [10X*[110X) if the row refers to data not belonging to the
  core part of the database (see Section [14X4.2-12[114X).[133X
  
  [33X[0;0YThe following optional arguments can be used to restrict the overviews.[133X
  
  [8X[3Xstd[103X[8X[108X
        [33X[0;6Ymust  be  a  positive integer or a list of positive integers; if it is
        given then only those representations are considered that refer to the
        [3Xstd[103X-th  set  of  standard  generators  or  the  [22Xi[122X-th  set  of standard
        generators, for [22Xi[122X in [3Xstd[103X (see Section [14X3.4[114X),[133X
  
  [8X[10X"contents"[110X[8X and [22Xsources[122X[108X
        [33X[0;6Yfor  a  string  or  a list of strings [22Xsources[122X, restrict the data about
        which  the  overview  is  formed; if [22Xsources[122X is the string [10X"core"[110X then
        only  data  from the [5XATLAS[105X of Group Representations are considered, if
        [22Xsources[122X  is  a  string that denotes a data extension in the sense of a
        [10Xdirid[110X  argument  of [2XAtlasOfGroupRepresentationsNotifyData[102X ([14X5.1-1[114X) then
        only  the data that belong to this data extension are considered; also
        a  list  of such strings may be given, then the union of these data is
        considered,[133X
  
  [8X[10XIdentifier[110X[8X and [22Xid[122X[108X
        [33X[0;6Yrestrict  to  representations  with  [10Xid[110X component in the list [22Xid[122X (note
        that  this  component  is  itself  a  list,  entering this list is not
        admissible), or satisfying the function [22Xid[122X,[133X
  
  [8X[10XIsPermGroup[110X[8X and [9Xtrue[109X (or [9Xfalse[109X)[108X
        [33X[0;6Yrestrict  to  permutation  representations (or to representations that
        are not permutation representations),[133X
  
  [8X[10XNrMovedPoints[110X[8X and [22Xn[122X[108X
        [33X[0;6Yfor  a positive integer, a list of positive integers, or a property [22Xn[122X,
        restrict  to  permutation  representations of degree equal to [22Xn[122X, or in
        the list [22Xn[122X, or satisfying the function [22Xn[122X,[133X
  
  [8X[10XNrMovedPoints[110X[8X and the string [10X"minimal"[110X[8X[108X
        [33X[0;6Yrestrict to faithful permutation representations of minimal degree (if
        this information is available),[133X
  
  [8X[10XIsTransitive[110X[8X and a boolean value[108X
        [33X[0;6Yrestrict  to  transitive  or  intransitive permutation representations
        where  this  information  is  available (if the value [9Xtrue[109X or [9Xfalse[109X is
        given),  or  to  representations  for  which  this  information is not
        available (if the value [9Xfail[109X is given),[133X
  
  [8X[10XIsPrimitive[110X[8X and a boolean value[108X
        [33X[0;6Yrestrict to primitive or imprimitive permutation representations where
        this  information  is available (if the value [9Xtrue[109X or [9Xfalse[109X is given),
        or  to representations for which this information is not available (if
        the value [9Xfail[109X is given),[133X
  
  [8X[10XTransitivity[110X[8X and [22Xn[122X[108X
        [33X[0;6Yfor  a  nonnegative  integer,  a  list  of  nonnegative integers, or a
        property  [22Xn[122X,  restrict  to  permutation  representations for which the
        information is available that the transitivity is equal to [22Xn[122X, or is in
        the list [22Xn[122X, or satisfies the function [22Xn[122X; if [22Xn[122X is [9Xfail[109X then restrict to
        all  permutation  representations  for  which  this information is not
        available,[133X
  
  [8X[10XRankAction[110X[8X and [22Xn[122X[108X
        [33X[0;6Yfor  a  nonnegative  integer,  a  list  of  nonnegative integers, or a
        property  [22Xn[122X,  restrict  to  permutation  representations for which the
        information  is  available  that  the rank is equal to [22Xn[122X, or is in the
        list [22Xn[122X, or satisfies the function [22Xn[122X; if [22Xn[122X is [9Xfail[109X then restrict to all
        permutation   representations   for  which  this  information  is  not
        available,[133X
  
  [8X[10XIsMatrixGroup[110X[8X and [9Xtrue[109X (or [9Xfalse[109X)[108X
        [33X[0;6Yrestrict to matrix representations (or to representations that are not
        matrix representations),[133X
  
  [8X[10XCharacteristic[110X[8X and [22Xp[122X[108X
        [33X[0;6Yfor  a  prime  integer,  a  list  of  prime integers, or a property [22Xp[122X,
        restrict to matrix representations over fields of characteristic equal
        to  [22Xp[122X, or in the list [22Xp[122X, or satisfying the function [22Xp[122X (representations
        over  residue  class  rings  that  are  not fields can be addressed by
        entering [9Xfail[109X as the value of [22Xp[122X),[133X
  
  [8X[10XDimension[110X[8X and [22Xn[122X[108X
        [33X[0;6Yfor  a positive integer, a list of positive integers, or a property [22Xn[122X,
        restrict  to matrix representations of dimension equal to [22Xn[122X, or in the
        list [22Xn[122X, or satisfying the function [22Xn[122X,[133X
  
  [8X[10XCharacteristic[110X[8X, [22Xp[122X, [10XDimension[110X[8X, and the string [10X"minimal"[110X[8X[108X
        [33X[0;6Yfor  a  prime  integer  [22Xp[122X, restrict to faithful matrix representations
        over  fields  of characteristic [22Xp[122X that have minimal dimension (if this
        information is available),[133X
  
  [8X[10XRing[110X[8X and [22XR[122X[108X
        [33X[0;6Yfor  a  ring  or  a property [22XR[122X, restrict to matrix representations for
        which the information is available that the ring spanned by the matrix
        entries  is  contained  in  this ring or satisfies this property (note
        that  the representation might be defined over a proper subring); if [22XR[122X
        is  [9Xfail[109X  then  restrict  to all matrix representations for which this
        information is not available,[133X
  
  [8X[10XRing[110X[8X, [22XR[122X, [10XDimension[110X[8X, and the string [10X"minimal"[110X[8X[108X
        [33X[0;6Yfor  a  ring  [22XR[122X, restrict to faithful matrix representations over this
        ring that have minimal dimension (if this information is available),[133X
  
  [8X[10XCharacter[110X[8X and [22Xchi[122X[108X
        [33X[0;6Yfor  a  class  function  or a list of class functions [22Xchi[122X, restrict to
        representations  with  these  characters  (note  that  the  underlying
        characteristic   of   the   class  function,  see  Section [14X'Reference:
        UnderlyingCharacteristic'[114X,   determines   the  characteristic  of  the
        representation),[133X
  
  [8X[10XCharacter[110X[8X and [22Xname[122X[108X
        [33X[0;6Yfor a string [22Xname[122X, restrict to representations for which the character
        is  known  to  have  this  name, according to the information shown by
        [2XDisplayAtlasInfo[102X;  if  the  characteristic  is  not  specified then it
        defaults to zero,[133X
  
  [8X[10XCharacter[110X[8X and [22Xn[122X[108X
        [33X[0;6Yfor  a  positive  integer [22Xn[122X, restrict to representations for which the
        character  is  known  to  be  the  [22Xn[122X-th irreducible character in [5XGAP[105X's
        library   character   table   of   the   group  in  question;  if  the
        characteristic is not specified then it defaults to zero,[133X
  
  [8X[10XIsStraightLineProgram[110X[8X and [9Xtrue[109X[108X
        [33X[0;6Yrestrict  to  straight  line  programs,  straight  line decisions (see
        Section [14X6.1[114X), and black box programs (see Section [14X6.2[114X), and[133X
  
  [8X[10XIsStraightLineProgram[110X[8X and [9Xfalse[109X[108X
        [33X[0;6Yrestrict to representations.[133X
  
  [33X[0;0YNote  that  the  above  conditions  refer  only  to  the information that is
  available  without  accessing the representations. For example, if it is not
  stored  in  the  table  of  contents whether a permutation representation is
  primitive  then  this representation does not match an [10XIsPrimitive[110X condition
  in [2XDisplayAtlasInfo[102X.[133X
  
  [33X[0;0YIf  [21Xminimality[121X  information  is  requested  and  no available representation
  matches this condition then either no minimal representation is available or
  the     information     about     the    minimality    is    missing.    See
  [2XMinimalRepresentationInfo[102X   ([14X6.3-1[114X)  for  checking  whether  the  minimality
  information  is  available for the group in question. Note that in the cases
  where  the string [10X"minimal"[110X occurs as an argument, [2XMinimalRepresentationInfo[102X
  ([14X6.3-1[114X)  is  called with third argument [10X"lookup"[110X; this is because the stored
  information  was  precomputed  just  for  the  groups  in the [5XATLAS[105X of Group
  Representations,  so  trying  to  compute  non-stored minimality information
  (using other available databases) will hardly be successful.[133X
  
  [33X[0;0YThe representations are ordered as follows. Permutation representations come
  first   (ordered   according   to   their   degrees),   followed  by  matrix
  representations  over  finite  fields  (ordered first according to the field
  size and second according to the dimension), matrix representations over the
  integers,  and  then  matrix representations over algebraic extension fields
  (both  kinds  ordered  according to the dimension), the last representations
  are matrix representations over residue class rings (ordered first according
  to the modulus and second according to the dimension).[133X
  
  [33X[0;0YThe  maximal  subgroups are ordered according to decreasing group order. For
  an extension [22XG.p[122X of a simple group [22XG[122X by an outer automorphism of prime order
  [22Xp[122X,  this  means  that  [22XG[122X  is  the  first  maximal subgroup and then come the
  extensions  of  the  maximal  subgroups  of [22XG[122X and the novelties; so the [22Xn[122X-th
  maximal  subgroup  of  [22XG[122X and the [22Xn[122X-th maximal subgroup of [22XG.p[122X are in general
  not related. (This coincides with the numbering used for the [2XMaxes[102X ([14XCTblLib:
  Maxes[114X) attribute for character tables.)[133X
  
  
  [1X3.6-2 [33X[0;0YExamples for DisplayAtlasInfo[133X[101X
  
  [33X[0;0YHere  are  some examples how [2XDisplayAtlasInfo[102X ([14X3.6-1[114X) can be called, and how
  its output can be interpreted.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XDisplayAtlasInfo( "contents" );[127X[104X
    [4X[28X- AtlasRepAccessRemoteFiles: false[128X[104X
    [4X[28X[128X[104X
    [4X[28X- AtlasRepDataDirectory: /home/you/gap/pkg/atlasrep/[128X[104X
    [4X[28X[128X[104X
    [4X[28XID       | address, version, files                        [128X[104X
    [4X[28X---------+------------------------------------------------[128X[104X
    [4X[28Xcore     | http://atlas.math.rwth-aachen.de/Atlas/,[128X[104X
    [4X[28X         | version 2019-04-08,                            [128X[104X
    [4X[28X         | 10586 files locally available.                 [128X[104X
    [4X[28X---------+------------------------------------------------[128X[104X
    [4X[28Xinternal | atlasrep/datapkg,                              [128X[104X
    [4X[28X         | version 2019-05-06,                            [128X[104X
    [4X[28X         | 276 files locally available.                   [128X[104X
    [4X[28X---------+------------------------------------------------[128X[104X
    [4X[28Xmfer     | http://www.math.rwth-aachen.de/~mfer/datagens/,[128X[104X
    [4X[28X         | version 2015-10-06,                            [128X[104X
    [4X[28X         | 34 files locally available.                    [128X[104X
    [4X[28X---------+------------------------------------------------[128X[104X
    [4X[28Xctblocks | ctblocks/atlas/,   [128X[104X
    [4X[28X         | version 2019-04-08,                            [128X[104X
    [4X[28X         | 121 files locally available.                   [128X[104X
  [4X[32X[104X
  
  [33X[0;0YNote:  The  above  output  does  not fit to the rest of the manual examples,
  since  data extensions except [10Xinternal[110X have been removed at the beginning of
  Chapter [14X2[114X.[133X
  
  [33X[0;0YThe  output tells us that two data extensions have been notified in addition
  to  the  core  data  from the [5XATLAS[105X of Group Representations and the (local)
  internal  data  distributed  with  the  [5XAtlasRep[105X  package.  The files of the
  extension [10Xmfer[110X must be downloaded before they can be read (but note that the
  access to remote files is disabled), and the files of the extension [10Xctblocks[110X
  are  locally available in the [11Xctblocks/atlas[111X subdirectory of the [5XGAP[105X package
  directory. This table (in particular the numbers of locally available files)
  depends  on  your  installation  of  the package and how many files you have
  already downloaded.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XDisplayAtlasInfo( [ "M11", "A5" ] );[127X[104X
    [4X[28Xgroup |  # | maxes | cl | cyc | out | fnd | chk | prs[128X[104X
    [4X[28X------+----+-------+----+-----+-----+-----+-----+----[128X[104X
    [4X[28XM11   | 42 |     5 |  + |  +  |     |  +  |  +  |  + [128X[104X
    [4X[28XA5*   | 18 |     3 |  + |     |     |     |  +  |  + [128X[104X
  [4X[32X[104X
  
  [33X[0;0YThe  above output means that the database provides [22X42[122X representations of the
  Mathieu  group  [22XM_11[122X,  straight  line  programs  for computing generators of
  representatives  of  all  five  classes  of maximal subgroups, for computing
  representatives  of  the  conjugacy classes of elements and of generators of
  maximally  cyclic  subgroups, contains no straight line program for applying
  outer   automorphisms  (well,  in  fact  [22XM_11[122X  admits  no  nontrivial  outer
  automorphism),  and  contains  straight  line  decisions that check a set of
  generators  or  a  set  of  group  elements  for  being  a  set  of standard
  generators. Analogously, [22X18[122X representations of the alternating group [22XA_5[122X are
  available,    straight   line   programs   for   computing   generators   of
  representatives  of  all three classes of maximal subgroups, and no straight
  line  programs  for  computing  representatives  of the conjugacy classes of
  elements,  of generators of maximally cyclic subgroups, and no for computing
  images  under  outer automorphisms; straight line decisions for checking the
  standardization of generators or group elements are available. The star [10X*[110X in
  the first column of the row for [22XA_5[122X means that some of the available data do
  not belong to the core part of the database (see Section [14X4.2-12[114X).[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XDisplayAtlasInfo( [ "M11", "A5" ], NrMovedPoints, 11 );[127X[104X
    [4X[28Xgroup | # | maxes | cl | cyc | out | fnd | chk | prs[128X[104X
    [4X[28X------+---+-------+----+-----+-----+-----+-----+----[128X[104X
    [4X[28XM11   | 1 |     5 |  + |  +  |     |  +  |  +  |  + [128X[104X
  [4X[32X[104X
  
  [33X[0;0YThe given conditions restrict the overview to permutation representations on
  [22X11[122X  points.  The  rows  for  all  those groups are omitted for which no such
  representation  is  available,  and the numbers of those representations are
  shown  that  satisfy the given conditions. In the above example, we see that
  no  representation  on  [22X11[122X points is available for [22XA_5[122X, and exactly one such
  representation is available for [22XM_11[122X.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XDisplayAtlasInfo( "A5", IsPermGroup, true );[127X[104X
    [4X[28XRepresentations for G = A5:    (all refer to std. generators 1)[128X[104X
    [4X[28X---------------------------[128X[104X
    [4X[28X1: G <= Sym(5)  3-trans., on cosets of A4 (1st max.)[128X[104X
    [4X[28X2: G <= Sym(6)  2-trans., on cosets of D10 (2nd max.)[128X[104X
    [4X[28X3: G <= Sym(10) rank 3, on cosets of S3 (3rd max.)[128X[104X
    [4X[25Xgap>[125X [27XDisplayAtlasInfo( "A5", NrMovedPoints, [ 4 .. 9 ] );[127X[104X
    [4X[28XRepresentations for G = A5:    (all refer to std. generators 1)[128X[104X
    [4X[28X---------------------------[128X[104X
    [4X[28X1: G <= Sym(5) 3-trans., on cosets of A4 (1st max.)[128X[104X
    [4X[28X2: G <= Sym(6) 2-trans., on cosets of D10 (2nd max.)[128X[104X
  [4X[32X[104X
  
  [33X[0;0YThe  first  three  representations  stored  for  [22XA_5[122X are (in fact primitive)
  permutation representations.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XDisplayAtlasInfo( "A5", Dimension, [ 1 .. 3 ] );[127X[104X
    [4X[28XRepresentations for G = A5:    (all refer to std. generators 1)[128X[104X
    [4X[28X---------------------------[128X[104X
    [4X[28X 8: G <= GL(2a,4)                character 2a[128X[104X
    [4X[28X 9: G <= GL(2b,4)                character 2b[128X[104X
    [4X[28X10: G <= GL(3,5)                 character 3a[128X[104X
    [4X[28X12: G <= GL(3a,9)                character 3a[128X[104X
    [4X[28X13: G <= GL(3b,9)                character 3b[128X[104X
    [4X[28X17: G <= GL(3a,Field([Sqrt(5)])) character 3a[128X[104X
    [4X[28X18: G <= GL(3b,Field([Sqrt(5)])) character 3b[128X[104X
    [4X[25Xgap>[125X [27XDisplayAtlasInfo( "A5", Characteristic, 0 );[127X[104X
    [4X[28XRepresentations for G = A5:    (all refer to std. generators 1)[128X[104X
    [4X[28X---------------------------[128X[104X
    [4X[28X14: G <= GL(4,Z)                 character 4a[128X[104X
    [4X[28X15: G <= GL(5,Z)                 character 5a[128X[104X
    [4X[28X16: G <= GL(6,Z)                 character 3ab[128X[104X
    [4X[28X17: G <= GL(3a,Field([Sqrt(5)])) character 3a[128X[104X
    [4X[28X18: G <= GL(3b,Field([Sqrt(5)])) character 3b[128X[104X
  [4X[32X[104X
  
  [33X[0;0YThe  representations  with number between [22X4[122X and [22X13[122X are (in fact irreducible)
  matrix  representations over various finite fields, those with numbers [22X14[122X to
  [22X16[122X  are  integral  matrix  representations,  and  the  last  two  are matrix
  representations over the field generated by [22Xsqrt{5}[122X over the rational number
  field.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XDisplayAtlasInfo( "A5", Identifier, "a" );[127X[104X
    [4X[28XRepresentations for G = A5:    (all refer to std. generators 1)[128X[104X
    [4X[28X---------------------------[128X[104X
    [4X[28X 4: G <= GL(4a,2)                character 4a[128X[104X
    [4X[28X 8: G <= GL(2a,4)                character 2a[128X[104X
    [4X[28X12: G <= GL(3a,9)                character 3a[128X[104X
    [4X[28X17: G <= GL(3a,Field([Sqrt(5)])) character 3a[128X[104X
  [4X[32X[104X
  
  [33X[0;0YEach  of  the  representations  with the numbers [22X4, 8, 12[122X, and [22X17[122X is labeled
  with the distinguishing letter [10Xa[110X.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XDisplayAtlasInfo( "A5", NrMovedPoints, IsPrimeInt );[127X[104X
    [4X[28XRepresentations for G = A5:    (all refer to std. generators 1)[128X[104X
    [4X[28X---------------------------[128X[104X
    [4X[28X1: G <= Sym(5) 3-trans., on cosets of A4 (1st max.)[128X[104X
    [4X[25Xgap>[125X [27XDisplayAtlasInfo( "A5", Characteristic, IsOddInt );[127X[104X
    [4X[28XRepresentations for G = A5:    (all refer to std. generators 1)[128X[104X
    [4X[28X---------------------------[128X[104X
    [4X[28X 6: G <= GL(4,3)  character 4a[128X[104X
    [4X[28X 7: G <= GL(6,3)  character 3ab[128X[104X
    [4X[28X10: G <= GL(3,5)  character 3a[128X[104X
    [4X[28X11: G <= GL(5,5)  character 5a[128X[104X
    [4X[28X12: G <= GL(3a,9) character 3a[128X[104X
    [4X[28X13: G <= GL(3b,9) character 3b[128X[104X
    [4X[25Xgap>[125X [27XDisplayAtlasInfo( "A5", Dimension, IsPrimeInt );[127X[104X
    [4X[28XRepresentations for G = A5:    (all refer to std. generators 1)[128X[104X
    [4X[28X---------------------------[128X[104X
    [4X[28X 8: G <= GL(2a,4)                character 2a[128X[104X
    [4X[28X 9: G <= GL(2b,4)                character 2b[128X[104X
    [4X[28X10: G <= GL(3,5)                 character 3a[128X[104X
    [4X[28X11: G <= GL(5,5)                 character 5a[128X[104X
    [4X[28X12: G <= GL(3a,9)                character 3a[128X[104X
    [4X[28X13: G <= GL(3b,9)                character 3b[128X[104X
    [4X[28X15: G <= GL(5,Z)                 character 5a[128X[104X
    [4X[28X17: G <= GL(3a,Field([Sqrt(5)])) character 3a[128X[104X
    [4X[28X18: G <= GL(3b,Field([Sqrt(5)])) character 3b[128X[104X
    [4X[25Xgap>[125X [27XDisplayAtlasInfo( "A5", Ring, IsFinite and IsPrimeField );[127X[104X
    [4X[28XRepresentations for G = A5:    (all refer to std. generators 1)[128X[104X
    [4X[28X---------------------------[128X[104X
    [4X[28X 4: G <= GL(4a,2) character 4a[128X[104X
    [4X[28X 5: G <= GL(4b,2) character 2ab[128X[104X
    [4X[28X 6: G <= GL(4,3)  character 4a[128X[104X
    [4X[28X 7: G <= GL(6,3)  character 3ab[128X[104X
    [4X[28X10: G <= GL(3,5)  character 3a[128X[104X
    [4X[28X11: G <= GL(5,5)  character 5a[128X[104X
  [4X[32X[104X
  
  [33X[0;0YThe above examples show how the output can be restricted using a property (a
  unary function that returns either [9Xtrue[109X or [9Xfalse[109X) that follows [2XNrMovedPoints[102X
  ([14XReference:  NrMovedPoints  for  a  permutation[114X), [2XCharacteristic[102X ([14XReference:
  Characteristic[114X), [2XDimension[102X ([14XReference: Dimension[114X), or [2XRing[102X ([14XReference: Ring[114X)
  in the argument list of [2XDisplayAtlasInfo[102X ([14X3.6-1[114X).[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XDisplayAtlasInfo( "A5", IsStraightLineProgram, true );[127X[104X
    [4X[28XPrograms for G = A5:    (all refer to std. generators 1)[128X[104X
    [4X[28X--------------------[128X[104X
    [4X[28X- class repres.*      [128X[104X
    [4X[28X- presentation        [128X[104X
    [4X[28X- maxes (all 3):[128X[104X
    [4X[28X  1:  A4              [128X[104X
    [4X[28X  2:  D10             [128X[104X
    [4X[28X  3:  S3              [128X[104X
    [4X[28X- std. gen. checker:[128X[104X
    [4X[28X  (check)             [128X[104X
    [4X[28X  (pres)              [128X[104X
  [4X[32X[104X
  
  [33X[0;0YStraight   line   programs   are   available  for  computing  generators  of
  representatives  of  the  three  classes  of maximal subgroups of [22XA_5[122X, and a
  straight  line  decision  for  checking whether given generators are in fact
  standard  generators  is  available  as  well  as a presentation in terms of
  standard  generators,  see [2XAtlasProgram[102X ([14X3.6-4[114X). A straight line program for
  computing  conjugacy class representatives is available, and the star [10X*[110X says
  that  this  program  does  not  belong to the core part of the database (see
  Section [14X4.2-12[114X).[133X
  
  [1X3.6-3 AtlasGenerators[101X
  
  [33X[1;0Y[29X[2XAtlasGenerators[102X( [3Xgapname[103X, [3Xrepnr[103X[, [3Xmaxnr[103X] ) [32X function[133X
  [33X[1;0Y[29X[2XAtlasGenerators[102X( [3Xidentifier[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Ya record containing generators for a representation, or [9Xfail[109X.[133X
  
  [33X[0;0YIn  the  first  form,  [3Xgapname[103X  must  be  a  string denoting a [5XGAP[105X name (see
  Section [14X3.3[114X)  of  a  group,  and [3Xrepnr[103X a positive integer. If at least [3Xrepnr[103X
  representations  for  the  group  with  [5XGAP[105X  name [3Xgapname[103X are available then
  [2XAtlasGenerators[102X,  when  called  with [3Xgapname[103X and [3Xrepnr[103X, returns an immutable
  record  describing  the [3Xrepnr[103X-th representation; otherwise [9Xfail[109X is returned.
  If  a  third  argument [3Xmaxnr[103X, a positive integer, is given then an immutable
  record  describing  the  restriction  of  the [3Xrepnr[103X-th representation to the
  [3Xmaxnr[103X-th maximal subgroup is returned.[133X
  
  [33X[0;0YThe result record has at least the following components.[133X
  
  [8X[10Xcontents[110X[8X[108X
        [33X[0;6Ythe  identifier  of  the  part of the database to which the generators
        belong, for example [10X"core"[110X or [10X"internal"[110X,[133X
  
  [8X[10Xgenerators[110X[8X[108X
        [33X[0;6Ya list of generators for the group,[133X
  
  [8X[10Xgroupname[110X[8X[108X
        [33X[0;6Ythe [5XGAP[105X name of the group (see Section [14X3.3[114X),[133X
  
  [8X[10Xidentifier[110X[8X[108X
        [33X[0;6Ya  [5XGAP[105X  object  (a list of filenames plus additional information) that
        uniquely determines the representation, see Section [14X7.7[114X; the value can
        be used as [10Xidentifier[110X argument of [2XAtlasGenerators[102X.[133X
  
  [8X[10Xrepname[110X[8X[108X
        [33X[0;6Ya string that is an initial part of the filenames of the generators.[133X
  
  [8X[10Xrepnr[110X[8X[108X
        [33X[0;6Ythe  number of the representation in the current session, equal to the
        argument [3Xrepnr[103X if this is given.[133X
  
  [8X[10Xstandardization[110X[8X[108X
        [33X[0;6Ythe positive integer denoting the underlying standard generators,[133X
  
  [8X[10Xtype[110X[8X[108X
        [33X[0;6Ya  string  that describes the type of the representation ([10X"perm"[110X for a
        permutation representation, [10X"matff"[110X for a matrix representation over a
        finite  field,  [10X"matint"[110X  for a matrix representation over the ring of
        integers,  [10X"matalg"[110X  for  a  matrix  representation  over an algebraic
        number field).[133X
  
  [33X[0;0YAdditionally,  the  following [13Xdescribing components[113X may be available if they
  are known, and depending on the data type of the representation.[133X
  
  [8X[10Xsize[110X[8X[108X
        [33X[0;6Ythe group order,[133X
  
  [8X[10Xid[110X[8X[108X
        [33X[0;6Ythe distinguishing string as described for [2XDisplayAtlasInfo[102X ([14X3.6-1[114X),[133X
  
  [8X[10Xcharactername[110X[8X[108X
        [33X[0;6Ya string that describes the character of the representation,[133X
  
  [8X[10Xconstituents[110X[8X[108X
        [33X[0;6Ya  list of positive integers denoting the positions of the irreducible
        constituents of the character of the representation,[133X
  
  [8X[10Xp[110X[8X (for permutation representations)[108X
        [33X[0;6Yfor the number of moved points,[133X
  
  [8X[10Xdim[110X[8X (for matrix representations)[108X
        [33X[0;6Ythe dimension of the matrices,[133X
  
  [8X[10Xring[110X[8X (for matrix representations)[108X
        [33X[0;6Ythe ring generated by the matrix entries,[133X
  
  [8X[10Xtransitivity[110X[8X (for permutation representations)[108X
        [33X[0;6Ya nonnegative integer, see [2XTransitivity[102X ([14XReference: Transitivity[114X),[133X
  
  [8X[10Xorbits[110X[8X (for intransitive permutation representations)[108X
        [33X[0;6Ythe sorted list of orbit lengths on the set of moved points,[133X
  
  [8X[10XrankAction[110X[8X (for transitive permutation representations)[108X
        [33X[0;6Ythe  number  of  orbits  of  the  point stabilizer on the set of moved
        points, see [2XRankAction[102X ([14XReference: RankAction[114X),[133X
  
  [8X[10Xstabilizer[110X[8X (for transitive permutation representations)[108X
        [33X[0;6Ya string that describes the structure of the point stabilizers,[133X
  
  [8X[10XisPrimitive[110X[8X (for transitive permutation representations)[108X
        [33X[0;6Y[9Xtrue[109X  if  the  point  stabilizers  are  maximal  subgroups,  and [9Xfalse[109X
        otherwise,[133X
  
  [8X[10Xmaxnr[110X[8X (for primitive permutation representations)[108X
        [33X[0;6Ythe  number  of the class of maximal subgroups that contains the point
        stabilizers, w. r. t. the [2XMaxes[102X ([14XCTblLib: Maxes[114X) list.[133X
  
  [33X[0;0YIt  should  be  noted  that  the  number [3Xrepnr[103X refers to the number shown by
  [2XDisplayAtlasInfo[102X  ([14X3.6-1[114X)  [13Xin  the current session[113X; it may be that after the
  addition  of  new  representations (for example after loading a package that
  provides some), [3Xrepnr[103X refers to another representation.[133X
  
  [33X[0;0YThe  alternative form of [2XAtlasGenerators[102X, with only argument [3Xidentifier[103X, can
  be  used  to  fetch  the  result  record  with  [10Xidentifier[110X  value  equal  to
  [3Xidentifier[103X. The purpose of this variant is to access the [13Xsame[113X representation
  also in [13Xdifferent[113X [5XGAP[105X sessions.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27Xgens1:= AtlasGenerators( "A5", 1 );[127X[104X
    [4X[28Xrec( charactername := "1a+4a", constituents := [ 1, 4 ], [128X[104X
    [4X[28X  contents := "core", generators := [ (1,2)(3,4), (1,3,5) ], [128X[104X
    [4X[28X  groupname := "A5", id := "", [128X[104X
    [4X[28X  identifier := [ "A5", [ "A5G1-p5B0.m1", "A5G1-p5B0.m2" ], 1, 5 ], [128X[104X
    [4X[28X  isPrimitive := true, maxnr := 1, p := 5, rankAction := 2, [128X[104X
    [4X[28X  repname := "A5G1-p5B0", repnr := 1, size := 60, stabilizer := "A4", [128X[104X
    [4X[28X  standardization := 1, transitivity := 3, type := "perm" )[128X[104X
    [4X[25Xgap>[125X [27Xgens8:= AtlasGenerators( "A5", 8 );[127X[104X
    [4X[28Xrec( charactername := "2a", constituents := [ 2 ], contents := "core",[128X[104X
    [4X[28X  dim := 2, [128X[104X
    [4X[28X  generators := [ [ [ Z(2)^0, 0*Z(2) ], [ Z(2^2), Z(2)^0 ] ], [128X[104X
    [4X[28X      [ [ 0*Z(2), Z(2)^0 ], [ Z(2)^0, Z(2)^0 ] ] ], groupname := "A5",[128X[104X
    [4X[28X  id := "a", [128X[104X
    [4X[28X  identifier := [ "A5", [ "A5G1-f4r2aB0.m1", "A5G1-f4r2aB0.m2" ], 1, [128X[104X
    [4X[28X      4 ], repname := "A5G1-f4r2aB0", repnr := 8, ring := GF(2^2), [128X[104X
    [4X[28X  size := 60, standardization := 1, type := "matff" )[128X[104X
    [4X[25Xgap>[125X [27Xgens17:= AtlasGenerators( "A5", 17 );[127X[104X
    [4X[28Xrec( charactername := "3a", constituents := [ 2 ], contents := "core",[128X[104X
    [4X[28X  dim := 3, [128X[104X
    [4X[28X  generators := [128X[104X
    [4X[28X    [ [ [ -1, 0, 0 ], [ 0, -1, 0 ], [ -E(5)-E(5)^4, -E(5)-E(5)^4, 1 ] [128X[104X
    [4X[28X         ], [ [ 0, 1, 0 ], [ 0, 0, 1 ], [ 1, 0, 0 ] ] ], [128X[104X
    [4X[28X  groupname := "A5", id := "a", [128X[104X
    [4X[28X  identifier := [ "A5", "A5G1-Ar3aB0.g", 1, 3 ], [128X[104X
    [4X[28X  polynomial := [ -1, 1, 1 ], repname := "A5G1-Ar3aB0", repnr := 17, [128X[104X
    [4X[28X  ring := NF(5,[ 1, 4 ]), size := 60, standardization := 1, [128X[104X
    [4X[28X  type := "matalg" )[128X[104X
  [4X[32X[104X
  
  [33X[0;0YEach of the above pairs of elements generates a group isomorphic to [22XA_5[122X.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27Xgens1max2:= AtlasGenerators( "A5", 1, 2 );[127X[104X
    [4X[28Xrec( charactername := "1a+4a", constituents := [ 1, 4 ], [128X[104X
    [4X[28X  contents := "core", generators := [ (1,2)(3,4), (2,3)(4,5) ], [128X[104X
    [4X[28X  groupname := "D10", id := "", [128X[104X
    [4X[28X  identifier := [ "A5", [ "A5G1-p5B0.m1", "A5G1-p5B0.m2" ], 1, 5, 2 ],[128X[104X
    [4X[28X  isPrimitive := true, maxnr := 1, p := 5, rankAction := 2, [128X[104X
    [4X[28X  repname := "A5G1-p5B0", repnr := 1, size := 10, stabilizer := "A4", [128X[104X
    [4X[28X  standardization := 1, transitivity := 3, type := "perm" )[128X[104X
    [4X[25Xgap>[125X [27Xid:= gens1max2.identifier;;[127X[104X
    [4X[25Xgap>[125X [27Xgens1max2 = AtlasGenerators( id );[127X[104X
    [4X[28Xtrue[128X[104X
    [4X[25Xgap>[125X [27Xmax2:= Group( gens1max2.generators );;[127X[104X
    [4X[25Xgap>[125X [27XSize( max2 );[127X[104X
    [4X[28X10[128X[104X
    [4X[25Xgap>[125X [27XIdGroup( max2 ) = IdGroup( DihedralGroup( 10 ) );[127X[104X
    [4X[28Xtrue[128X[104X
  [4X[32X[104X
  
  [33X[0;0YThe  elements stored in [10Xgens1max2.generators[110X describe the restriction of the
  first  representation  of  [22XA_5[122X  to  a  group  in the second class of maximal
  subgroups   of   [22XA_5[122X   according   to  the  list  in  the  [5XATLAS[105X  of  Finite
  Groups [CCN+85]; this subgroup is isomorphic to the dihedral group [22XD_10[122X.[133X
  
  [1X3.6-4 AtlasProgram[101X
  
  [33X[1;0Y[29X[2XAtlasProgram[102X( [3Xgapname[103X[, [3Xstd[103X][, [3X"contents"[103X, [3Xsources[103X][, [3X"version"[103X, [3Xvers[103X], [3X...[103X ) [32X function[133X
  [33X[1;0Y[29X[2XAtlasProgram[102X( [3Xidentifier[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Ya record containing a program, or [9Xfail[109X.[133X
  
  [33X[0;0YIn  the  first  form,  [3Xgapname[103X  must  be  a  string denoting a [5XGAP[105X name (see
  Section [14X3.3[114X)  of  a  group  [22XG[122X, say. If the database contains a straight line
  program  (see  Section [14X'Reference: Straight Line Programs'[114X) or straight line
  decision  (see  Section [14X6.1[114X)  or  black  box  program  (see  Section [14X6.2[114X) as
  described  by  the  arguments indicated by [3X...[103X (see below) then [2XAtlasProgram[102X
  returns  an  immutable  record  containing  this  program. Otherwise [9Xfail[109X is
  returned.[133X
  
  [33X[0;0YIf   the   optional   argument  [3Xstd[103X  is  given,  only  those  straight  line
  programs/decisions  are  considered that take generators from the [3Xstd[103X-th set
  of standard generators of [22XG[122X as input, see Section [14X3.4[114X.[133X
  
  [33X[0;0YIf  the  optional arguments [10X"contents"[110X and [3Xsources[103X are given then the latter
  must  be  either  a  string  or  a list of strings, with the same meaning as
  described for [2XDisplayAtlasInfo[102X ([14X3.6-1[114X).[133X
  
  [33X[0;0YIf  the optional arguments [10X"version"[110X and [3Xvers[103X are given then the latter must
  be  either  a  number  or  a  list  of numbers, and only those straight line
  programs/decisions are considered whose version number fits to [3Xvers[103X.[133X
  
  [33X[0;0YThe result record has at least the following components.[133X
  
  [8X[10Xgroupname[110X[8X[108X
        [33X[0;6Ythe string [3Xgapname[103X,[133X
  
  [8X[10Xidentifier[110X[8X[108X
        [33X[0;6Ya  [5XGAP[105X  object  (a list of filenames plus additional information) that
        uniquely  determines  the program; the value can be used as [3Xidentifier[103X
        argument of [2XAtlasProgram[102X (see below),[133X
  
  [8X[10Xprogram[110X[8X[108X
        [33X[0;6Ythe required straight line program/decision, or black box program,[133X
  
  [8X[10Xstandardization[110X[8X[108X
        [33X[0;6Ythe positive integer denoting the underlying standard generators of [22XG[122X,[133X
  
  [8X[10Xversion[110X[8X[108X
        [33X[0;6Ythe  substring of the filename of the program that denotes the version
        of the program.[133X
  
  [33X[0;0YIf  the program computes generators of the restriction to a maximal subgroup
  then also the following components are present.[133X
  
  [8X[10Xsize[110X[8X[108X
        [33X[0;6Ythe order of the maximal subgroup,[133X
  
  [8X[10Xsubgroupname[110X[8X[108X
        [33X[0;6Ya string denoting a name of the maximal subgroup.[133X
  
  [33X[0;0YIn the first form, the arguments indicated by [3X...[103X must be as follows.[133X
  
  [8X(the string [10X"maxes"[110X[8X and) a positive integer [22Xmaxnr[122X [108X
        [33X[0;6Ythe  required  program  computes  generators  of  the [22Xmaxnr[122X-th maximal
        subgroup of the group with [5XGAP[105X name [22Xgapname[122X.[133X
  
        [33X[0;6YIn  this  case,  the  result record of [2XAtlasProgram[102X also may contain a
        component  [10Xsize[110X,  whose  value is the order of the maximal subgroup in
        question.[133X
  
  [8Xthe string [10X"maxes"[110X[8X and two positive integers [22Xmaxnr[122X and [22Xstd2[122X[108X
        [33X[0;6Ythe  required  program  computes  standard  generators of the [22Xmaxnr[122X-th
        maximal  subgroup  of  the  group  with [5XGAP[105X name [22Xgapname[122X, w. r. t. the
        standardization [22Xstd2[122X.[133X
  
        [33X[0;6YA  prescribed  [10X"version"[110X parameter refers to the straight line program
        for  computing  the  restriction, not to the program for standardizing
        the result of the restriction.[133X
  
        [33X[0;6YThe  meaning  of  the component [10Xsize[110X in the result, if present, is the
        same as in the previous case.[133X
  
  [8Xthe string [10X"maxstd"[110X[8X and three positive integers [22Xmaxnr[122X, [22Xvers[122X, [22Xsubstd[122X[108X
        [33X[0;6Ythe  required  program  computes  standard  generators of the [22Xmaxnr[122X-th
        maximal    subgroup    of    the   group   with   [5XGAP[105X   name   [22Xgapname[122X
        w. r. t. standardization  [22Xsubstd[122X;  in  this  case,  the  inputs of the
        program are [13Xnot[113X standard generators of the group with [5XGAP[105X name [22Xgapname[122X
        but  the  outputs  of  the straight line program with version [22Xvers[122X for
        computing generators of its [22Xmaxnr[122X-th maximal subgroup.[133X
  
  [8Xthe string [10X"kernel"[110X[8X and a string [22Xfactname[122X[108X
        [33X[0;6Ythe   required  program  computes  generators  of  the  kernel  of  an
        epimorphism from [22XG[122X to a group with [5XGAP[105X name [22Xfactname[122X.[133X
  
  [8Xone of the strings [10X"classes"[110X[8X or [10X"cyclic"[110X[8X[108X
        [33X[0;6Ythe  required program computes representatives of conjugacy classes of
        elements   or   representatives  of  generators  of  maximally  cyclic
        subgroups of [22XG[122X, respectively.[133X
  
        [33X[0;6YSee [BSWW01]  and [SWW00] for the background concerning these straight
        line  programs. In these cases, the result record of [2XAtlasProgram[102X also
        contains  a component [10Xoutputs[110X, whose value is a list of class names of
        the outputs, as described in Section [14X3.5[114X.[133X
  
  [8Xthe string [10X"cyc2ccl"[110X[8X (and the string [22Xvers[122X)[108X
        [33X[0;6Ythe  required program computes representatives of conjugacy classes of
        elements  from  representatives  of  generators  of  maximally  cyclic
        subgroups of [22XG[122X. Thus the inputs are the outputs of the program of type
        [10X"cyclic"[110X whose version is [22Xvers[122X.[133X
  
  [8Xthe strings [10X"cyc2ccl"[110X[8X, [22Xvers1[122X, [10X"version"[110X[8X, [22Xvers2[122X[108X
        [33X[0;6Ythe  required program computes representatives of conjugacy classes of
        elements  from  representatives  of  generators  of  maximally  cyclic
        subgroups  of  [22XG[122X,  where  the inputs are the outputs of the program of
        type  [10X"cyclic"[110X  whose version is [22Xvers1[122X and the required program itself
        has version [22Xvers2[122X.[133X
  
  [8Xthe strings [10X"automorphism"[110X[8X and [22Xautname[122X[108X
        [33X[0;6Ythe  required program computes images of standard generators under the
        outer automorphism of [22XG[122X that is given by this string.[133X
  
        [33X[0;6YNote  that  a  value  [10X"2"[110X  of  [22Xautname[122X  means  that  the square of the
        automorphism  is  an  inner  automorphism  of  [22XG[122X  (not necessarily the
        identity mapping) but the automorphism itself is not.[133X
  
  [8Xthe string [10X"check"[110X[8X[108X
        [33X[0;6Ythe  required  result is a straight line decision that takes a list of
        generators  for  [22XG[122X  and  returns [9Xtrue[109X if these generators are standard
        generators of [22XG[122X w. r. t. the standardization [3Xstd[103X, and [9Xfalse[109X otherwise.[133X
  
  [8Xthe string [10X"presentation"[110X[8X[108X
        [33X[0;6Ythe  required  result is a straight line decision that takes a list of
        group  elements  and  returns  [9Xtrue[109X  if  these  elements  are standard
        generators of [22XG[122X w. r. t. the standardization [3Xstd[103X, and [9Xfalse[109X otherwise.[133X
  
        [33X[0;6YSee [2XStraightLineProgramFromStraightLineDecision[102X ([14X6.1-9[114X) for an example
        how  to  derive  defining  relators  for  [22XG[122X  in  terms of the standard
        generators from such a straight line decision.[133X
  
  [8Xthe string [10X"find"[110X[8X[108X
        [33X[0;6Ythe  required result is a black box program that takes [22XG[122X and returns a
        list of standard generators of [22XG[122X, w. r. t. the standardization [3Xstd[103X.[133X
  
  [8Xthe string [10X"restandardize"[110X[8X and an integer [22Xstd2[122X[108X
        [33X[0;6Ythe  required result is a straight line program that computes standard
        generators  of [22XG[122X w. r. t. the [22Xstd2[122X-th set of standard generators of [22XG[122X;
        in this case, the argument [3Xstd[103X must be given.[133X
  
  [8Xthe strings [10X"other"[110X[8X and [22Xdescr[122X[108X
        [33X[0;6Ythe required program is described by [22Xdescr[122X.[133X
  
  [33X[0;0YThe second form of [2XAtlasProgram[102X, with only argument the list [3Xidentifier[103X, can
  be  used  to  fetch  the  result  record  with  [10Xidentifier[110X  value  equal  to
  [3Xidentifier[103X.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27Xprog:= AtlasProgram( "A5", 2 );[127X[104X
    [4X[28Xrec( groupname := "A5", identifier := [ "A5", "A5G1-max2W1", 1 ], [128X[104X
    [4X[28X  program := <straight line program>, size := 10, [128X[104X
    [4X[28X  standardization := 1, subgroupname := "D10", version := "1" )[128X[104X
    [4X[25Xgap>[125X [27XStringOfResultOfStraightLineProgram( prog.program, [ "a", "b" ] );[127X[104X
    [4X[28X"[ a, bbab ]"[128X[104X
    [4X[25Xgap>[125X [27Xgens1:= AtlasGenerators( "A5", 1 );[127X[104X
    [4X[28Xrec( charactername := "1a+4a", constituents := [ 1, 4 ], [128X[104X
    [4X[28X  contents := "core", generators := [ (1,2)(3,4), (1,3,5) ], [128X[104X
    [4X[28X  groupname := "A5", id := "", [128X[104X
    [4X[28X  identifier := [ "A5", [ "A5G1-p5B0.m1", "A5G1-p5B0.m2" ], 1, 5 ], [128X[104X
    [4X[28X  isPrimitive := true, maxnr := 1, p := 5, rankAction := 2, [128X[104X
    [4X[28X  repname := "A5G1-p5B0", repnr := 1, size := 60, stabilizer := "A4", [128X[104X
    [4X[28X  standardization := 1, transitivity := 3, type := "perm" )[128X[104X
    [4X[25Xgap>[125X [27Xmaxgens:= ResultOfStraightLineProgram( prog.program,[127X[104X
    [4X[25X>[125X [27X                 gens1.generators );[127X[104X
    [4X[28X[ (1,2)(3,4), (2,3)(4,5) ][128X[104X
    [4X[25Xgap>[125X [27Xmaxgens = gens1max2.generators;[127X[104X
    [4X[28Xtrue[128X[104X
  [4X[32X[104X
  
  [33X[0;0YThe  above  example  shows  that  for  restricting  representations given by
  standard  generators  to  a  maximal  subgroup of [22XA_5[122X, we can also fetch and
  apply the appropriate straight line program. Such a program (see [14X'Reference:
  Straight  Line  Programs'[114X)  takes  standard  generators  of a group –in this
  example  [22XA_5[122X– as its input, and returns a list of elements in this group –in
  this  example  generators  of  the [22XD_10[122X subgroup we had met above– which are
  computed essentially by evaluating structured words in terms of the standard
  generators.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27Xprog:= AtlasProgram( "J1", "cyclic" );[127X[104X
    [4X[28Xrec( groupname := "J1", identifier := [ "J1", "J1G1-cycW1", 1 ], [128X[104X
    [4X[28X  outputs := [ "6A", "7A", "10B", "11A", "15B", "19A" ], [128X[104X
    [4X[28X  program := <straight line program>, standardization := 1, [128X[104X
    [4X[28X  version := "1" )[128X[104X
    [4X[25Xgap>[125X [27Xgens:= GeneratorsOfGroup( FreeGroup( "x", "y" ) );;[127X[104X
    [4X[25Xgap>[125X [27XResultOfStraightLineProgram( prog.program, gens );[127X[104X
    [4X[28X[ (x*y)^2*((y*x)^2*y^2*x)^2*y^2, x*y, (x*(y*x*y)^2)^2*y, [128X[104X
    [4X[28X  (x*y*x*(y*x*y)^3*x*y^2)^2*x*y*x*(y*x*y)^2*y, x*y*x*(y*x*y)^2*y, [128X[104X
    [4X[28X  (x*y)^2*y ][128X[104X
  [4X[32X[104X
  
  [33X[0;0YThe  above  example  shows  how  to fetch and use straight line programs for
  computing  generators  of representatives of maximally cyclic subgroups of a
  given group.[133X
  
  [1X3.6-5 AtlasProgramInfo[101X
  
  [33X[1;0Y[29X[2XAtlasProgramInfo[102X( [3Xgapname[103X[, [3Xstd[103X][, [3X"contents"[103X, [3Xsources[103X][, [3X"version"[103X, [3Xvers[103X], [3X...[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Ya record describing a program, or [9Xfail[109X.[133X
  
  [33X[0;0Y[2XAtlasProgramInfo[102X  takes  the  same  arguments  as  [2XAtlasProgram[102X ([14X3.6-4[114X), and
  returns  a  similar result. The only difference is that the records returned
  by [2XAtlasProgramInfo[102X have no components [10Xprogram[110X and [10Xoutputs[110X. The idea is that
  one  can use [2XAtlasProgramInfo[102X for testing whether the program in question is
  available at all, but without downloading files. The [10Xidentifier[110X component of
  the  result  of  [2XAtlasProgramInfo[102X can then be used to fetch the program with
  [2XAtlasProgram[102X ([14X3.6-4[114X).[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XAtlasProgramInfo( "J1", "cyclic" );[127X[104X
    [4X[28Xrec( groupname := "J1", identifier := [ "J1", "J1G1-cycW1", 1 ], [128X[104X
    [4X[28X  standardization := 1, version := "1" )[128X[104X
  [4X[32X[104X
  
  [1X3.6-6 OneAtlasGeneratingSetInfo[101X
  
  [33X[1;0Y[29X[2XOneAtlasGeneratingSetInfo[102X( [[3Xgapname[103X][,] [[3Xstd[103X][,] [[3X...[103X] ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Ya   record   describing   a   representation  that  satisfies  the
            conditions, or [9Xfail[109X.[133X
  
  [33X[0;0YLet  [3Xgapname[103X be a string denoting a [5XGAP[105X name (see Section [14X3.3[114X) of a group [22XG[122X,
  say.  If  the  database  contains at least one representation for [22XG[122X with the
  required  properties then [2XOneAtlasGeneratingSetInfo[102X returns a record [22Xr[122X whose
  components  are the same as those of the records returned by [2XAtlasGenerators[102X
  ([14X3.6-3[114X),  except  that  the  component  [10Xgenerators[110X  is not contained, and an
  additional component [10XgivenRing[110X is present if [10XRing[110X is one of the arguments in
  the function call.[133X
  
  [33X[0;0YThe  information  in  [10XgivenRing[110X  can be used later to construct the matrices
  over  the  prescribed  ring. Note that this ring may be for example a domain
  constructed  with [2XAlgebraicExtension[102X ([14XReference: AlgebraicExtension[114X) instead
  of  a  field  of  cyclotomics  or  of  a  finite  field  constructed with [2XGF[102X
  ([14XReference: GF for field size[114X).[133X
  
  [33X[0;0YThe  component  [10Xidentifier[110X  of  [22Xr[122X  can  be used as input for [2XAtlasGenerators[102X
  ([14X3.6-3[114X)  in  order  to fetch the generators. If no representation satisfying
  the given conditions is available then [9Xfail[109X is returned.[133X
  
  [33X[0;0YIf the argument [3Xstd[103X is given then it must be a positive integer or a list of
  positive  integers,  denoting the sets of standard generators w. r. t. which
  the representation shall be given (see Section [14X3.4[114X).[133X
  
  [33X[0;0YThe  argument  [3Xgapname[103X  can  be  missing  (then  all  available  groups  are
  considered), or a list of group names can be given instead.[133X
  
  [33X[0;0YFurther  restrictions  can be entered as arguments, with the same meaning as
  described     for     [2XDisplayAtlasInfo[102X     ([14X3.6-1[114X).     The     result    of
  [2XOneAtlasGeneratingSetInfo[102X  describes  the  first  generating  set for [22XG[122X that
  matches the restrictions, in the ordering shown by [2XDisplayAtlasInfo[102X ([14X3.6-1[114X).[133X
  
  [33X[0;0YNote    that    even    in    the    case    that    the   user   preference
  [10XAtlasRepAccessRemoteFiles[110X   has   the   value   [9Xtrue[109X   (see  Section [14X4.2-1[114X),
  [2XOneAtlasGeneratingSetInfo[102X  does  [13Xnot[113X  attempt to [13Xtransfer[113X remote data files,
  just  the  table  of  contents  is  evaluated.  So this function (as well as
  [2XAllAtlasGeneratingSetInfos[102X   ([14X3.6-7[114X))   can   be   used  to  check  for  the
  availability  of  certain  representations,  and  afterwards  one  can  call
  [2XAtlasGenerators[102X ([14X3.6-3[114X) for those representations one wants to work with.[133X
  
  [33X[0;0YIn  the  following  example,  we try to access information about permutation
  representations for the alternating group [22XA_5[122X.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27Xinfo:= OneAtlasGeneratingSetInfo( "A5" );[127X[104X
    [4X[28Xrec( charactername := "1a+4a", constituents := [ 1, 4 ], [128X[104X
    [4X[28X  contents := "core", groupname := "A5", id := "", [128X[104X
    [4X[28X  identifier := [ "A5", [ "A5G1-p5B0.m1", "A5G1-p5B0.m2" ], 1, 5 ], [128X[104X
    [4X[28X  isPrimitive := true, maxnr := 1, p := 5, rankAction := 2, [128X[104X
    [4X[28X  repname := "A5G1-p5B0", repnr := 1, size := 60, stabilizer := "A4", [128X[104X
    [4X[28X  standardization := 1, transitivity := 3, type := "perm" )[128X[104X
    [4X[25Xgap>[125X [27Xgens:= AtlasGenerators( info.identifier );[127X[104X
    [4X[28Xrec( charactername := "1a+4a", constituents := [ 1, 4 ], [128X[104X
    [4X[28X  contents := "core", generators := [ (1,2)(3,4), (1,3,5) ], [128X[104X
    [4X[28X  groupname := "A5", id := "", [128X[104X
    [4X[28X  identifier := [ "A5", [ "A5G1-p5B0.m1", "A5G1-p5B0.m2" ], 1, 5 ], [128X[104X
    [4X[28X  isPrimitive := true, maxnr := 1, p := 5, rankAction := 2, [128X[104X
    [4X[28X  repname := "A5G1-p5B0", repnr := 1, size := 60, stabilizer := "A4", [128X[104X
    [4X[28X  standardization := 1, transitivity := 3, type := "perm" )[128X[104X
    [4X[25Xgap>[125X [27Xinfo = OneAtlasGeneratingSetInfo( "A5", IsPermGroup, true );[127X[104X
    [4X[28Xtrue[128X[104X
    [4X[25Xgap>[125X [27Xinfo = OneAtlasGeneratingSetInfo( "A5", NrMovedPoints, "minimal" );[127X[104X
    [4X[28Xtrue[128X[104X
    [4X[25Xgap>[125X [27Xinfo = OneAtlasGeneratingSetInfo( "A5", NrMovedPoints, [ 1 .. 10 ] );[127X[104X
    [4X[28Xtrue[128X[104X
    [4X[25Xgap>[125X [27XOneAtlasGeneratingSetInfo( "A5", NrMovedPoints, 20 );[127X[104X
    [4X[28Xfail[128X[104X
  [4X[32X[104X
  
  [33X[0;0YNote  that  a  permutation  representation of degree [22X20[122X could be obtained by
  taking  twice  the  primitive  representation  on  [22X10[122X  points;  however, the
  database does not store this imprimitive representation (cf. Section [14X3.2[114X).[133X
  
  [33X[0;0YWe continue this example. Next we access matrix representations of [22XA_5[122X.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27Xinfo:= OneAtlasGeneratingSetInfo( "A5", IsMatrixGroup, true );[127X[104X
    [4X[28Xrec( charactername := "4a", constituents := [ 4 ], contents := "core",[128X[104X
    [4X[28X  dim := 4, groupname := "A5", id := "a", [128X[104X
    [4X[28X  identifier := [ "A5", [ "A5G1-f2r4aB0.m1", "A5G1-f2r4aB0.m2" ], 1, [128X[104X
    [4X[28X      2 ], repname := "A5G1-f2r4aB0", repnr := 4, ring := GF(2), [128X[104X
    [4X[28X  size := 60, standardization := 1, type := "matff" )[128X[104X
    [4X[25Xgap>[125X [27Xgens:= AtlasGenerators( info.identifier );[127X[104X
    [4X[28Xrec( charactername := "4a", constituents := [ 4 ], contents := "core",[128X[104X
    [4X[28X  dim := 4, [128X[104X
    [4X[28X  generators := [ <an immutable 4x4 matrix over GF2>, [128X[104X
    [4X[28X      <an immutable 4x4 matrix over GF2> ], groupname := "A5", [128X[104X
    [4X[28X  id := "a", [128X[104X
    [4X[28X  identifier := [ "A5", [ "A5G1-f2r4aB0.m1", "A5G1-f2r4aB0.m2" ], 1, [128X[104X
    [4X[28X      2 ], repname := "A5G1-f2r4aB0", repnr := 4, ring := GF(2), [128X[104X
    [4X[28X  size := 60, standardization := 1, type := "matff" )[128X[104X
    [4X[25Xgap>[125X [27Xinfo = OneAtlasGeneratingSetInfo( "A5", Dimension, 4 );[127X[104X
    [4X[28Xtrue[128X[104X
    [4X[25Xgap>[125X [27Xinfo = OneAtlasGeneratingSetInfo( "A5", Characteristic, 2 );[127X[104X
    [4X[28Xtrue[128X[104X
    [4X[25Xgap>[125X [27Xinfo2:= OneAtlasGeneratingSetInfo( "A5", Ring, GF(2) );;[127X[104X
    [4X[25Xgap>[125X [27Xinfo.identifier = info2.identifier; [127X[104X
    [4X[28Xtrue[128X[104X
    [4X[25Xgap>[125X [27XOneAtlasGeneratingSetInfo( "A5", Characteristic, [2,5], Dimension, 2 );[127X[104X
    [4X[28Xrec( charactername := "2a", constituents := [ 2 ], contents := "core",[128X[104X
    [4X[28X  dim := 2, groupname := "A5", id := "a", [128X[104X
    [4X[28X  identifier := [ "A5", [ "A5G1-f4r2aB0.m1", "A5G1-f4r2aB0.m2" ], 1, [128X[104X
    [4X[28X      4 ], repname := "A5G1-f4r2aB0", repnr := 8, ring := GF(2^2), [128X[104X
    [4X[28X  size := 60, standardization := 1, type := "matff" )[128X[104X
    [4X[25Xgap>[125X [27XOneAtlasGeneratingSetInfo( "A5", Characteristic, [2,5], Dimension, 1 );[127X[104X
    [4X[28Xfail[128X[104X
    [4X[25Xgap>[125X [27Xinfo:= OneAtlasGeneratingSetInfo( "A5", Characteristic, 0,[127X[104X
    [4X[25X>[125X [27X                                           Dimension, 4 );[127X[104X
    [4X[28Xrec( charactername := "4a", constituents := [ 4 ], contents := "core",[128X[104X
    [4X[28X  dim := 4, groupname := "A5", id := "", [128X[104X
    [4X[28X  identifier := [ "A5", "A5G1-Zr4B0.g", 1, 4 ], [128X[104X
    [4X[28X  repname := "A5G1-Zr4B0", repnr := 14, ring := Integers, size := 60, [128X[104X
    [4X[28X  standardization := 1, type := "matint" )[128X[104X
    [4X[25Xgap>[125X [27Xgens:= AtlasGenerators( info.identifier );[127X[104X
    [4X[28Xrec( charactername := "4a", constituents := [ 4 ], contents := "core",[128X[104X
    [4X[28X  dim := 4, [128X[104X
    [4X[28X  generators := [128X[104X
    [4X[28X    [ [128X[104X
    [4X[28X      [ [ 1, 0, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 1, 0, 0 ], [128X[104X
    [4X[28X          [ -1, -1, -1, -1 ] ], [128X[104X
    [4X[28X      [ [ 0, 1, 0, 0 ], [ 0, 0, 0, 1 ], [ 0, 0, 1, 0 ], [128X[104X
    [4X[28X          [ 1, 0, 0, 0 ] ] ], groupname := "A5", id := "", [128X[104X
    [4X[28X  identifier := [ "A5", "A5G1-Zr4B0.g", 1, 4 ], [128X[104X
    [4X[28X  repname := "A5G1-Zr4B0", repnr := 14, ring := Integers, size := 60, [128X[104X
    [4X[28X  standardization := 1, type := "matint" )[128X[104X
    [4X[25Xgap>[125X [27Xinfo = OneAtlasGeneratingSetInfo( "A5", Ring, Integers );[127X[104X
    [4X[28Xtrue[128X[104X
    [4X[25Xgap>[125X [27Xinfo2:= OneAtlasGeneratingSetInfo( "A5", Ring, CF(37) );;[127X[104X
    [4X[25Xgap>[125X [27Xinfo = info2;[127X[104X
    [4X[28Xfalse[128X[104X
    [4X[25Xgap>[125X [27XDifference( RecNames( info2 ), RecNames( info ) );[127X[104X
    [4X[28X[ "givenRing" ][128X[104X
    [4X[25Xgap>[125X [27Xinfo2.givenRing;[127X[104X
    [4X[28XCF(37)[128X[104X
    [4X[25Xgap>[125X [27XOneAtlasGeneratingSetInfo( "A5", Ring, Integers mod 77 );[127X[104X
    [4X[28Xfail[128X[104X
    [4X[25Xgap>[125X [27Xinfo:= OneAtlasGeneratingSetInfo( "A5", Ring, CF(5), Dimension, 3 );[127X[104X
    [4X[28Xrec( charactername := "3a", constituents := [ 2 ], contents := "core",[128X[104X
    [4X[28X  dim := 3, givenRing := CF(5), groupname := "A5", id := "a", [128X[104X
    [4X[28X  identifier := [ "A5", "A5G1-Ar3aB0.g", 1, 3 ], [128X[104X
    [4X[28X  polynomial := [ -1, 1, 1 ], repname := "A5G1-Ar3aB0", repnr := 17, [128X[104X
    [4X[28X  ring := NF(5,[ 1, 4 ]), size := 60, standardization := 1, [128X[104X
    [4X[28X  type := "matalg" )[128X[104X
    [4X[25Xgap>[125X [27Xgens:= AtlasGenerators( info );[127X[104X
    [4X[28Xrec( charactername := "3a", constituents := [ 2 ], contents := "core",[128X[104X
    [4X[28X  dim := 3, [128X[104X
    [4X[28X  generators := [128X[104X
    [4X[28X    [ [ [ -1, 0, 0 ], [ 0, -1, 0 ], [ -E(5)-E(5)^4, -E(5)-E(5)^4, 1 ] [128X[104X
    [4X[28X         ], [ [ 0, 1, 0 ], [ 0, 0, 1 ], [ 1, 0, 0 ] ] ], [128X[104X
    [4X[28X  givenRing := CF(5), groupname := "A5", id := "a", [128X[104X
    [4X[28X  identifier := [ "A5", "A5G1-Ar3aB0.g", 1, 3 ], [128X[104X
    [4X[28X  polynomial := [ -1, 1, 1 ], repname := "A5G1-Ar3aB0", repnr := 17, [128X[104X
    [4X[28X  ring := NF(5,[ 1, 4 ]), size := 60, standardization := 1, [128X[104X
    [4X[28X  type := "matalg" )[128X[104X
    [4X[25Xgap>[125X [27Xgens2:= AtlasGenerators( info.identifier );;[127X[104X
    [4X[25Xgap>[125X [27XDifference( RecNames( gens ), RecNames( gens2 ) );[127X[104X
    [4X[28X[ "givenRing" ][128X[104X
    [4X[25Xgap>[125X [27XOneAtlasGeneratingSetInfo( "A5", Ring, GF(17) );[127X[104X
    [4X[28Xfail[128X[104X
  [4X[32X[104X
  
  [1X3.6-7 AllAtlasGeneratingSetInfos[101X
  
  [33X[1;0Y[29X[2XAllAtlasGeneratingSetInfos[102X( [[3Xgapname[103X][,] [[3Xstd[103X][,] [[3X...[103X] ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Ythe  list  of  all records describing representations that satisfy
            the conditions.[133X
  
  [33X[0;0Y[2XAllAtlasGeneratingSetInfos[102X  is similar to [2XOneAtlasGeneratingSetInfo[102X ([14X3.6-6[114X).
  The  difference  is  that  the  list of [13Xall[113X records describing the available
  representations  with  the  given properties is returned instead of just one
  such  component.  In  particular  an  empty  list  is  returned  if  no such
  representation is available.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XAllAtlasGeneratingSetInfos( "A5", IsPermGroup, true );[127X[104X
    [4X[28X[ rec( charactername := "1a+4a", constituents := [ 1, 4 ], [128X[104X
    [4X[28X      contents := "core", groupname := "A5", id := "", [128X[104X
    [4X[28X      identifier := [ "A5", [ "A5G1-p5B0.m1", "A5G1-p5B0.m2" ], 1, 5 ][128X[104X
    [4X[28X        , isPrimitive := true, maxnr := 1, p := 5, rankAction := 2, [128X[104X
    [4X[28X      repname := "A5G1-p5B0", repnr := 1, size := 60, [128X[104X
    [4X[28X      stabilizer := "A4", standardization := 1, transitivity := 3, [128X[104X
    [4X[28X      type := "perm" ), [128X[104X
    [4X[28X  rec( charactername := "1a+5a", constituents := [ 1, 5 ], [128X[104X
    [4X[28X      contents := "core", groupname := "A5", id := "", [128X[104X
    [4X[28X      identifier := [ "A5", [ "A5G1-p6B0.m1", "A5G1-p6B0.m2" ], 1, 6 ][128X[104X
    [4X[28X        , isPrimitive := true, maxnr := 2, p := 6, rankAction := 2, [128X[104X
    [4X[28X      repname := "A5G1-p6B0", repnr := 2, size := 60, [128X[104X
    [4X[28X      stabilizer := "D10", standardization := 1, transitivity := 2, [128X[104X
    [4X[28X      type := "perm" ), [128X[104X
    [4X[28X  rec( charactername := "1a+4a+5a", constituents := [ 1, 4, 5 ], [128X[104X
    [4X[28X      contents := "core", groupname := "A5", id := "", [128X[104X
    [4X[28X      identifier := [ "A5", [ "A5G1-p10B0.m1", "A5G1-p10B0.m2" ], 1, [128X[104X
    [4X[28X          10 ], isPrimitive := true, maxnr := 3, p := 10, [128X[104X
    [4X[28X      rankAction := 3, repname := "A5G1-p10B0", repnr := 3, [128X[104X
    [4X[28X      size := 60, stabilizer := "S3", standardization := 1, [128X[104X
    [4X[28X      transitivity := 1, type := "perm" ) ][128X[104X
  [4X[32X[104X
  
  [33X[0;0YNote  that  a matrix representation in any characteristic can be obtained by
  reducing  a permutation representation or an integral matrix representation;
  however,  the  database  does  not [13Xstore[113X such a representation (cf. Section 
  [14X3.2[114X).[133X
  
  
  [1X3.6-8 [33X[0;0YAtlasGroup[133X[101X
  
  [33X[1;0Y[29X[2XAtlasGroup[102X( [[3Xgapname[103X][,] [[3Xstd[103X][,] [[3X...[103X] ) [32X function[133X
  [33X[1;0Y[29X[2XAtlasGroup[102X( [3Xidentifier[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Ya group that satisfies the conditions, or [9Xfail[109X.[133X
  
  [33X[0;0Y[2XAtlasGroup[102X  takes  the  same arguments as [2XOneAtlasGeneratingSetInfo[102X ([14X3.6-6[114X),
  and  returns  the  group generated by the [10Xgenerators[110X component of the record
  that  is returned by [2XOneAtlasGeneratingSetInfo[102X ([14X3.6-6[114X) with these arguments;
  if  [2XOneAtlasGeneratingSetInfo[102X  ([14X3.6-6[114X)  returns  [9Xfail[109X  then  also [2XAtlasGroup[102X
  returns [9Xfail[109X.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27Xg:= AtlasGroup( "A5" );[127X[104X
    [4X[28XGroup([ (1,2)(3,4), (1,3,5) ])[128X[104X
  [4X[32X[104X
  
  [33X[0;0YAlternatively,  it  is  possible  to  enter  exactly  one argument, a record
  [3Xidentifier[103X    as    returned   by   [2XOneAtlasGeneratingSetInfo[102X   ([14X3.6-6[114X)   or
  [2XAllAtlasGeneratingSetInfos[102X  ([14X3.6-7[114X),  or  the [10Xidentifier[110X component of such a
  record.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27Xinfo:= OneAtlasGeneratingSetInfo( "A5" );[127X[104X
    [4X[28Xrec( charactername := "1a+4a", constituents := [ 1, 4 ], [128X[104X
    [4X[28X  contents := "core", groupname := "A5", id := "", [128X[104X
    [4X[28X  identifier := [ "A5", [ "A5G1-p5B0.m1", "A5G1-p5B0.m2" ], 1, 5 ], [128X[104X
    [4X[28X  isPrimitive := true, maxnr := 1, p := 5, rankAction := 2, [128X[104X
    [4X[28X  repname := "A5G1-p5B0", repnr := 1, size := 60, stabilizer := "A4", [128X[104X
    [4X[28X  standardization := 1, transitivity := 3, type := "perm" )[128X[104X
    [4X[25Xgap>[125X [27XAtlasGroup( info );[127X[104X
    [4X[28XGroup([ (1,2)(3,4), (1,3,5) ])[128X[104X
    [4X[25Xgap>[125X [27XAtlasGroup( info.identifier );[127X[104X
    [4X[28XGroup([ (1,2)(3,4), (1,3,5) ])[128X[104X
  [4X[32X[104X
  
  [33X[0;0YIn   the   groups  returned  by  [2XAtlasGroup[102X,  the  value  of  the  attribute
  [2XAtlasRepInfoRecord[102X  ([14X3.6-10[114X) is set. This information is used for example by
  [2XAtlasSubgroup[102X  ([14X3.6-9[114X)  when  this function is called with second argument a
  group created by [2XAtlasGroup[102X.[133X
  
  
  [1X3.6-9 [33X[0;0YAtlasSubgroup[133X[101X
  
  [33X[1;0Y[29X[2XAtlasSubgroup[102X( [3Xgapname[103X[, [3Xstd[103X][, [3X...[103X], [3Xmaxnr[103X ) [32X function[133X
  [33X[1;0Y[29X[2XAtlasSubgroup[102X( [3Xidentifier[103X, [3Xmaxnr[103X ) [32X function[133X
  [33X[1;0Y[29X[2XAtlasSubgroup[102X( [3XG[103X, [3Xmaxnr[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Ya group that satisfies the conditions, or [9Xfail[109X.[133X
  
  [33X[0;0YThe arguments of [2XAtlasSubgroup[102X, except the last argument [3Xmaxnr[103X, are the same
  as  for [2XAtlasGroup[102X ([14X3.6-8[114X). If the database provides a straight line program
  for  restricting  representations  of  the  group  with  name [3Xgapname[103X (given
  w. r. t. the  [3Xstd[103X-th  standard  generators) to the [3Xmaxnr[103X-th maximal subgroup
  and  if  a  representation with the required properties is available, in the
  sense  that  calling [2XAtlasGroup[102X ([14X3.6-8[114X) with the same arguments except [3Xmaxnr[103X
  yields   a  group,  then  [2XAtlasSubgroup[102X  returns  the  restriction  of  this
  representation to the [3Xmaxnr[103X-th maximal subgroup.[133X
  
  [33X[0;0YIn all other cases, [9Xfail[109X is returned.[133X
  
  [33X[0;0YNote  that the conditions refer to the group and not to the subgroup. It may
  happen  that  in  the  restriction  of  a  permutation  representation  to a
  subgroup,  fewer  points  are  moved,  or  that  the restriction of a matrix
  representation  turns  out  to  be  defined  over a smaller ring. Here is an
  example.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27Xg:= AtlasSubgroup( "A5", NrMovedPoints, 5, 1 );[127X[104X
    [4X[28XGroup([ (1,5)(2,3), (1,3,5) ])[128X[104X
    [4X[25Xgap>[125X [27XNrMovedPoints( g );[127X[104X
    [4X[28X4[128X[104X
  [4X[32X[104X
  
  [33X[0;0YAlternatively,  it  is  possible  to  enter exactly two arguments, the first
  being  a  record [3Xidentifier[103X as returned by [2XOneAtlasGeneratingSetInfo[102X ([14X3.6-6[114X)
  or [2XAllAtlasGeneratingSetInfos[102X ([14X3.6-7[114X), or the [10Xidentifier[110X component of such a
  record, or a group [3XG[103X constructed with [2XAtlasGroup[102X ([14X3.6-8[114X).[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27Xinfo:= OneAtlasGeneratingSetInfo( "A5" );[127X[104X
    [4X[28Xrec( charactername := "1a+4a", constituents := [ 1, 4 ], [128X[104X
    [4X[28X  contents := "core", groupname := "A5", id := "", [128X[104X
    [4X[28X  identifier := [ "A5", [ "A5G1-p5B0.m1", "A5G1-p5B0.m2" ], 1, 5 ], [128X[104X
    [4X[28X  isPrimitive := true, maxnr := 1, p := 5, rankAction := 2, [128X[104X
    [4X[28X  repname := "A5G1-p5B0", repnr := 1, size := 60, stabilizer := "A4", [128X[104X
    [4X[28X  standardization := 1, transitivity := 3, type := "perm" )[128X[104X
    [4X[25Xgap>[125X [27XAtlasSubgroup( info, 1 );[127X[104X
    [4X[28XGroup([ (1,5)(2,3), (1,3,5) ])[128X[104X
    [4X[25Xgap>[125X [27XAtlasSubgroup( info.identifier, 1 );[127X[104X
    [4X[28XGroup([ (1,5)(2,3), (1,3,5) ])[128X[104X
    [4X[25Xgap>[125X [27XAtlasSubgroup( AtlasGroup( "A5" ), 1 );[127X[104X
    [4X[28XGroup([ (1,5)(2,3), (1,3,5) ])[128X[104X
  [4X[32X[104X
  
  [1X3.6-10 AtlasRepInfoRecord[101X
  
  [33X[1;0Y[29X[2XAtlasRepInfoRecord[102X( [3XG[103X ) [32X attribute[133X
  [33X[1;0Y[29X[2XAtlasRepInfoRecord[102X( [3Xname[103X ) [32X attribute[133X
  [6XReturns:[106X  [33X[0;10Ythe  record  stored  in the group [3XG[103X when this was constructed with
            [2XAtlasGroup[102X  ([14X3.6-8[114X),  or a record with information about the group
            with name [3Xname[103X.[133X
  
  [33X[0;0YFor  a  group [3XG[103X that has been constructed with [2XAtlasGroup[102X ([14X3.6-8[114X), the value
  of  this  attribute  is  the info record that describes [3XG[103X, in the sense that
  this  record was the first argument of the call to [2XAtlasGroup[102X ([14X3.6-8[114X), or it
  is  the  result  of  the  call to [2XOneAtlasGeneratingSetInfo[102X ([14X3.6-6[114X) with the
  conditions that were listed in the call to [2XAtlasGroup[102X ([14X3.6-8[114X).[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XAtlasRepInfoRecord( AtlasGroup( "A5" ) );[127X[104X
    [4X[28Xrec( charactername := "1a+4a", constituents := [ 1, 4 ], [128X[104X
    [4X[28X  contents := "core", groupname := "A5", id := "", [128X[104X
    [4X[28X  identifier := [ "A5", [ "A5G1-p5B0.m1", "A5G1-p5B0.m2" ], 1, 5 ], [128X[104X
    [4X[28X  isPrimitive := true, maxnr := 1, p := 5, rankAction := 2, [128X[104X
    [4X[28X  repname := "A5G1-p5B0", repnr := 1, size := 60, stabilizer := "A4", [128X[104X
    [4X[28X  standardization := 1, transitivity := 3, type := "perm" )[128X[104X
  [4X[32X[104X
  
  [33X[0;0YFor  a  string [3Xname[103X that is a [5XGAP[105X name of a group [22XG[122X, say, [2XAtlasRepInfoRecord[102X
  returns  a  record  that  contains  information  about  [22XG[122X  which  is used by
  [2XDisplayAtlasInfo[102X  ([14X3.6-1[114X).  The  following  components  may  be bound in the
  record.[133X
  
  [8X[10Xname[110X[8X[108X
        [33X[0;6Ythe string [3Xname[103X,[133X
  
  [8X[10XnrMaxes[110X[8X[108X
        [33X[0;6Ythe number of conjugacy classes of maximal subgroups of [22XG[122X,[133X
  
  [8X[10Xsize[110X[8X[108X
        [33X[0;6Ythe order of [22XG[122X,[133X
  
  [8X[10XsizesMaxes[110X[8X[108X
        [33X[0;6Ya list which contains at position [22Xi[122X, if bound, the order of a subgroup
        in the [22Xi[122X-th class of maximal subgroups of [22XG[122X,[133X
  
  [8X[10XslpMaxes[110X[8X[108X
        [33X[0;6Ya  list  of  length two; the first entry is a list of positions [22Xi[122X such
        that  a  straight  line  program  for  computing  the  restriction  of
        representations  of  [22XG[122X  to  a  subgroup  in  the [22Xi[122X-th class of maximal
        subgroups   is  available  via  [5XAtlasRep[105X;  the  second  entry  is  the
        corresponding  list  of  standardizations  of  the generators of [22XG[122X for
        which these straight line programs are available,[133X
  
  [8X[10XstructureMaxes[110X[8X[108X
        [33X[0;6Ya list which contains at position [22Xi[122X, if bound, a string that describes
        the  structure of the subgroups in the [22Xi[122X-th class of maximal subgroups
        of [22XG[122X.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XAtlasRepInfoRecord( "A5" );[127X[104X
    [4X[28Xrec( name := "A5", nrMaxes := 3, size := 60, [128X[104X
    [4X[28X  sizesMaxes := [ 12, 10, 6 ], [128X[104X
    [4X[28X  slpMaxes := [ [ 1 .. 3 ], [ [ 1 ], [ 1 ], [ 1 ] ] ], [128X[104X
    [4X[28X  structureMaxes := [ "A4", "D10", "S3" ] )[128X[104X
    [4X[25Xgap>[125X [27XAtlasRepInfoRecord( "J5" );[127X[104X
    [4X[28Xrec(  )[128X[104X
  [4X[32X[104X
  
  
  [1X3.6-11 [33X[0;0YEvaluatePresentation[133X[101X
  
  [33X[1;0Y[29X[2XEvaluatePresentation[102X( [3XG[103X, [3Xgapname[103X[, [3Xstd[103X] ) [32X operation[133X
  [33X[1;0Y[29X[2XEvaluatePresentation[102X( [3Xgens[103X, [3Xgapname[103X[, [3Xstd[103X] ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ya list of group elements or [9Xfail[109X.[133X
  
  [33X[0;0YThe  first  argument  must  be  either  a  group  [3XG[103X  or a list [3Xgens[103X of group
  generators,  and  [3Xgapname[103X  must  be  a  string  that  is  a  [5XGAP[105X  name  (see
  Section [14X3.3[114X) of a group [22XH[122X, say. The optional argument [3Xstd[103X, if given, must be
  a  positive  integer  that denotes a standardization of generators of [22XH[122X, the
  default is [22X1[122X.[133X
  
  [33X[0;0Y[2XEvaluatePresentation[102X  returns  [9Xfail[109X  if  no  presentation for [22XH[122X w. r. t. the
  standardization  [3Xstd[103X  is  stored  in the database, and otherwise returns the
  list  of  results of evaluating the relators of a presentation for [22XH[122X at [3Xgens[103X
  or   the   [2XGeneratorsOfGroup[102X  ([14XReference:  GeneratorsOfGroup[114X)  value  of  [3XG[103X,
  respectively.  (An  error  is  signalled  if the number of generators is not
  equal to the number of inputs of the presentation.)[133X
  
  [33X[0;0YThe  result  can  be used as follows. Let [22XN[122X be the normal closure of the the
  result  in  [3XG[103X.  The  factor  group  [3XG[103X[22X/N[122X  is  an  epimorphic  image  of [22XH[122X. In
  particular,  if  all  entries of the result have order [22X1[122X then [3XG[103X itself is an
  epimorphic  image  of  [22XH[122X.  Moreover,  an epimorphism is given by mapping the
  [3Xstd[103X-th  standard  generators of [22XH[122X to the [22XN[122X-cosets of the given generators of
  [3XG[103X.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27Xg:= MathieuGroup( 12 );;[127X[104X
    [4X[25Xgap>[125X [27Xgens:= GeneratorsOfGroup( g );;  # switch to 2 generators[127X[104X
    [4X[25Xgap>[125X [27Xg:= Group( gens[1] * gens[3], gens[2] * gens[3] );;[127X[104X
    [4X[25Xgap>[125X [27XEvaluatePresentation( g, "J0" );  # no pres. for group "J0"[127X[104X
    [4X[28Xfail[128X[104X
    [4X[25Xgap>[125X [27Xrelimgs:= EvaluatePresentation( g, "M11" );;[127X[104X
    [4X[25Xgap>[125X [27XList( relimgs, Order );  # wrong group[127X[104X
    [4X[28X[ 3, 1, 5, 4, 10 ][128X[104X
    [4X[25Xgap>[125X [27Xrelimgs:= EvaluatePresentation( g, "M12" );;[127X[104X
    [4X[25Xgap>[125X [27XList( relimgs, Order );  # generators are not standard[127X[104X
    [4X[28X[ 3, 4, 5, 4, 4 ][128X[104X
    [4X[25Xgap>[125X [27Xg:= AtlasGroup( "M12" );;[127X[104X
    [4X[25Xgap>[125X [27Xrelimgs:= EvaluatePresentation( g, "M12", 1 );;[127X[104X
    [4X[25Xgap>[125X [27XList( relimgs, Order );  # right group, std. generators[127X[104X
    [4X[28X[ 1, 1, 1, 1, 1 ][128X[104X
    [4X[25Xgap>[125X [27Xg:= AtlasGroup( "2.M12" );;[127X[104X
    [4X[25Xgap>[125X [27Xrelimgs:= EvaluatePresentation( g, "M12", 1 );;[127X[104X
    [4X[25Xgap>[125X [27XList( relimgs, Order );  # std. generators for extension[127X[104X
    [4X[28X[ 1, 2, 1, 1, 2 ][128X[104X
    [4X[25Xgap>[125X [27XSize( NormalClosure( g, SubgroupNC( g, relimgs ) ) );[127X[104X
    [4X[28X2[128X[104X
  [4X[32X[104X
  
  
  [1X3.6-12 [33X[0;0YStandardGeneratorsData[133X[101X
  
  [33X[1;0Y[29X[2XStandardGeneratorsData[102X( [3XG[103X, [3Xgapname[103X[, [3Xstd[103X] ) [32X operation[133X
  [33X[1;0Y[29X[2XStandardGeneratorsData[102X( [3Xgens[103X, [3Xgapname[103X[, [3Xstd[103X] ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Ya  record  that  describes  standard  generators  of  the group in
            question, or [9Xfail[109X, or the string [10X"timeout"[110X.[133X
  
  [33X[0;0YThe  first  argument  must  be  either  a  group  [3XG[103X  or a list [3Xgens[103X of group
  generators,  and  [3Xgapname[103X  must  be  a  string  that  is  a  [5XGAP[105X  name  (see
  Section [14X3.3[114X) of a group [22XH[122X, say. The optional argument [3Xstd[103X, if given, must be
  a  positive  integer  that denotes a standardization of generators of [22XH[122X, the
  default is [22X1[122X.[133X
  
  [33X[0;0YIf  the  global  option  [10Xprojective[110X is given then the group elements must be
  matrices  over  a finite field, and the group must be a central extension of
  the  group  [22XH[122X by a normal subgroup that consists of scalar matrices. In this
  case,  all  computations  will  be  carried  out  modulo scalar matrices (in
  particular,   element   orders   will   be  computed  using  [2XProjectiveOrder[102X
  ([14XReference:  ProjectiveOrder[114X)),  and  the  returned standard generators will
  belong to [22XH[122X.[133X
  
  [33X[0;0Y[2XStandardGeneratorsData[102X returns[133X
  
  [8X[9Xfail[109X[108X
        [33X[0;6Yif  no  black  box  program  for  computing  standard  generators of [22XH[122X
        w. r. t. the  standardization [3Xstd[103X is stored in the database, or if the
        black box program returns [9Xfail[109X because a runtime error occurred or the
        program  has proved that the given group or generators cannot generate
        a group isomorphic to [22XH[122X,[133X
  
  [8X[10X"timeout"[110X[8X[108X
        [33X[0;6Yif  the  black  box  program returns [10X"timeout"[110X, typically because some
        elements  of a given order were not found among a reasonable number of
        random elements, or[133X
  
  [8Xa record containing standard generators[108X
        [33X[0;6Yotherwise.[133X
  
  [33X[0;0YWhen the result is not a record then either the group is not isomorphic to [22XH[122X
  (modulo  scalars  if  applicable),  or  we were unlucky with choosing random
  elements.[133X
  
  [33X[0;0YWhen   a  record  is  returned  [13Xand[113X  [3XG[103X  or  the  group  generated  by  [3Xgens[103X,
  respectively,  is isomorphic to [22XH[122X (or to a central extension of [22XH[122X by a group
  of scalar matrices if the global option [10Xprojective[110X is given) then the result
  describes the desired standard generators.[133X
  
  [33X[0;0YIf  [3XG[103X  or  the group generated by [3Xgens[103X, respectively, is [13Xnot[113X isomorphic to [22XH[122X
  then it may still happen that [2XStandardGeneratorsData[102X returns a record. For a
  proof  that  the  returned record describes the desired standard generators,
  one  can  use  a presentation of [22XH[122X whose generators correspond to the [3Xstd[103X-th
  standard generators, see [2XEvaluatePresentation[102X ([14X3.6-11[114X).[133X
  
  [33X[0;0YA returned record has the following components.[133X
  
  [8X[10Xgapname[110X[8X[108X
        [33X[0;6Ythe string [3Xgapname[103X,[133X
  
  [8X[10Xgivengens[110X[8X[108X
        [33X[0;6Ythe  list  of  group  generators  from  which standard generators were
        computed,   either   [3Xgens[103X   or   the   [2XGeneratorsOfGroup[102X   ([14XReference:
        GeneratorsOfGroup[114X) value of [3XG[103X,[133X
  
  [8X[10Xstdgens[110X[8X[108X
        [33X[0;6Ya list of standard generators of the group,[133X
  
  [8X[10Xgivengenstostdgens[110X[8X[108X
        [33X[0;6Ya  straight  line  program that takes [10Xgivengens[110X as inputs, and returns
        [10Xstdgens[110X,[133X
  
  [8X[10Xstd[110X[8X[108X
        [33X[0;6Ythe underlying standardization [3Xstd[103X.[133X
  
  [33X[0;0YThe first examples show three cases of failure, due to the unavailability of
  a suitable black box program or to a wrong choice of [3Xgapname[103X. (In the search
  for  standard  generators of [22XM_11[122X in the group [22XM_12[122X, one may or may not find
  an  element  whose  order  does  not  appear in [22XM_11[122X; in the first case, the
  result  is [9Xfail[109X, whereas a record is returned in the second case. Both cases
  occur.)[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27XStandardGeneratorsData( MathieuGroup( 11 ), "J0" );[127X[104X
    [4X[28Xfail[128X[104X
    [4X[25Xgap>[125X [27XStandardGeneratorsData( MathieuGroup( 11 ), "M12" );[127X[104X
    [4X[28X"timeout"[128X[104X
    [4X[25Xgap>[125X [27Xrepeat[127X[104X
    [4X[25X>[125X [27X     res:= StandardGeneratorsData( MathieuGroup( 12 ), "M11" );[127X[104X
    [4X[25X>[125X [27X   until res = fail;[127X[104X
  [4X[32X[104X
  
  [33X[0;0YThe  next example shows a computation of standard generators for the Mathieu
  group [22XM_12[122X. Using a presentation of [22XM_12[122X w. r. t. these standard generators,
  we prove that the given group is isomorphic to [22XM_12[122X.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27Xgens:= GeneratorsOfGroup( MathieuGroup( 12 ) );;[127X[104X
    [4X[25Xgap>[125X [27Xstd:= 1;;[127X[104X
    [4X[25Xgap>[125X [27Xres:= StandardGeneratorsData( gens, "M12", std );;[127X[104X
    [4X[25Xgap>[125X [27XSet( RecNames( res ) );[127X[104X
    [4X[28X[ "gapname", "givengens", "givengenstostdgens", "std", "stdgens" ][128X[104X
    [4X[25Xgap>[125X [27Xgens = res.givengens;[127X[104X
    [4X[28Xtrue[128X[104X
    [4X[25Xgap>[125X [27XResultOfStraightLineProgram( res.givengenstostdgens, gens )[127X[104X
    [4X[25X>[125X [27X   = res.stdgens;[127X[104X
    [4X[28Xtrue[128X[104X
    [4X[25Xgap>[125X [27Xevl:= EvaluatePresentation( res.stdgens, "M12", std );;[127X[104X
    [4X[25Xgap>[125X [27XForAll( evl, IsOne );[127X[104X
    [4X[28Xtrue[128X[104X
  [4X[32X[104X
  
  [33X[0;0YThe  next  example shows the use of the global option [10Xprojective[110X. We take an
  irreducible  matrix  representation of the double cover of the Mathieu group
  [22XM_12[122X  (thus  the  center  is  represented  by  scalar  matrices) and compute
  standard  generators  of the factor group [22XM_12[122X. Using a presentation of [22XM_12[122X
  w. r. t. these  standard generators, we prove that the given group is modulo
  scalars isomorphic to [22XM_12[122X, and we get generators for the kernel.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27Xg:= AtlasGroup( "2.M12", IsMatrixGroup, Characteristic, IsPosInt );;[127X[104X
    [4X[25Xgap>[125X [27Xgens:= Permuted( GeneratorsOfGroup( g ), (1,2) );;[127X[104X
    [4X[25Xgap>[125X [27Xres:= StandardGeneratorsData( gens, "M12", std : projective );;[127X[104X
    [4X[25Xgap>[125X [27Xgens = res.givengens;[127X[104X
    [4X[28Xtrue[128X[104X
    [4X[25Xgap>[125X [27XResultOfStraightLineProgram( res.givengenstostdgens, gens )[127X[104X
    [4X[25X>[125X [27X   = res.stdgens;[127X[104X
    [4X[28Xtrue[128X[104X
    [4X[25Xgap>[125X [27Xevl:= EvaluatePresentation( res.stdgens, "M12", std );;[127X[104X
    [4X[25Xgap>[125X [27XForAll( evl, IsOne );[127X[104X
    [4X[28Xfalse[128X[104X
    [4X[25Xgap>[125X [27XForAll( evl, x -> IsCentral( g, x ) );[127X[104X
    [4X[28Xtrue[128X[104X
  [4X[32X[104X
  
  
  [1X3.7 [33X[0;0Y[5XBrowse[105X[101X[1X Applications Provided by [5XAtlasRep[105X[101X[1X[133X[101X
  
  [33X[0;0YThe functions [2XBrowseMinimalDegrees[102X ([14X3.7-1[114X), [2XBrowseBibliographySporadicSimple[102X
  ([14X3.7-2[114X),  and  [2XBrowseAtlasInfo[102X  ([14XBrowse: BrowseAtlasInfo[114X) (an alternative to
  [2XDisplayAtlasInfo[102X  ([14X3.6-1[114X)) are available only if the [5XGAP[105X package [5XBrowse[105X (see
  [BL26]) is loaded.[133X
  
  [1X3.7-1 BrowseMinimalDegrees[101X
  
  [33X[1;0Y[29X[2XBrowseMinimalDegrees[102X( [[3Xgapnames[103X] ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Ythe list of info records for the clicked representations.[133X
  
  [33X[0;0YIf  the  [5XGAP[105X  package  [5XBrowse[105X  (see  [BL26]) is loaded then this function is
  available.  It  opens a browse table whose rows correspond to the groups for
  which  [5XAtlasRep[105X  knows some information about minimal degrees, whose columns
  correspond  to  the  characteristics  that  occur, and whose entries are the
  known minimal degrees.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27Xif IsBound( BrowseMinimalDegrees ) then[127X[104X
    [4X[25X>[125X [27X  down:= NCurses.keys.DOWN;;  DOWN:= NCurses.keys.NPAGE;;[127X[104X
    [4X[25X>[125X [27X  right:= NCurses.keys.RIGHT;;  END:= NCurses.keys.END;;[127X[104X
    [4X[25X>[125X [27X  enter:= NCurses.keys.ENTER;;  nop:= [ 14, 14, 14 ];;[127X[104X
    [4X[25X>[125X [27X  # just scroll in the table[127X[104X
    [4X[25X>[125X [27X  BrowseData.SetReplay( Concatenation( [ DOWN, DOWN, DOWN,[127X[104X
    [4X[25X>[125X [27X         right, right, right ], "sedddrrrddd", nop, nop, "Q" ) );[127X[104X
    [4X[25X>[125X [27X  BrowseMinimalDegrees();;[127X[104X
    [4X[25X>[125X [27X  # restrict the table to the groups with minimal ordinary degree 6[127X[104X
    [4X[25X>[125X [27X  BrowseData.SetReplay( Concatenation( "scf6",[127X[104X
    [4X[25X>[125X [27X       [ down, down, right, enter, enter ] , nop, nop, "Q" ) );[127X[104X
    [4X[25X>[125X [27X  BrowseMinimalDegrees();;[127X[104X
    [4X[25X>[125X [27X  BrowseData.SetReplay( false );[127X[104X
    [4X[25X>[125X [27Xfi;[127X[104X
  [4X[32X[104X
  
  [33X[0;0YIf  an  argument  [3Xgapnames[103X  is  given then it must be a list of [5XGAP[105X names of
  groups.  The  browse  table  is then restricted to the rows corresponding to
  these  group  names and to the columns that are relevant for these groups. A
  perhaps  interesting  example  is  the  subtable  with  the  data concerning
  sporadic  simple  groups and their covering groups, which has been published
  in [Jan05]. This table can be shown as follows.[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27Xif IsBound( BrowseMinimalDegrees ) then[127X[104X
    [4X[25X>[125X [27X  # just scroll in the table[127X[104X
    [4X[25X>[125X [27X  BrowseData.SetReplay( Concatenation( [ DOWN, DOWN, DOWN, END ],[127X[104X
    [4X[25X>[125X [27X         "rrrrrrrrrrrrrr", nop, nop, "Q" ) );[127X[104X
    [4X[25X>[125X [27X  BrowseMinimalDegrees( BibliographySporadicSimple.groupNamesJan05 );;[127X[104X
    [4X[25X>[125X [27Xfi;[127X[104X
  [4X[32X[104X
  
  [33X[0;0YThe  browse  table  does  [13Xnot[113X  contain  rows for the groups [22X6.M_22[122X, [22X12.M_22[122X,
  [22X6.Fi_22[122X.  Note that in spite of the title of [Jan05], the entries in Table 1
  of  this  paper  are  in  fact  the  minimal degrees of faithful [13Xirreducible[113X
  representations, and in the above three cases, these degrees are larger than
  the  minimal degrees of faithful representations. The underlying data of the
  browse table is about the minimal faithful (but not necessarily irreducible)
  degrees.[133X
  
  [33X[0;0YThe    return    value    of    [2XBrowseMinimalDegrees[102X    is   the   list   of
  [2XOneAtlasGeneratingSetInfo[102X ([14X3.6-6[114X) values for those representations that have
  been [21Xclicked[121X in visual mode.[133X
  
  [33X[0;0YThe variant without arguments of this function is also available in the menu
  shown by [2XBrowseGapData[102X ([14XBrowse: BrowseGapData[114X).[133X
  
  [1X3.7-2 BrowseBibliographySporadicSimple[101X
  
  [33X[1;0Y[29X[2XBrowseBibliographySporadicSimple[102X(  ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Ya    record   as   returned   by   [2XParseBibXMLExtString[102X   ([14XGAPDoc:
            ParseBibXMLextString[114X).[133X
  
  [33X[0;0YIf  the  [5XGAP[105X  package  [5XBrowse[105X  (see  [BL26]) is loaded then this function is
  available.  It  opens a browse table whose rows correspond to the entries of
  the  bibliographies  in the [5XATLAS[105X of Finite Groups [CCN+85] and in the [5XATLAS[105X
  of Brauer Characters [JLPW95].[133X
  
  [33X[0;0YThe  function  is  based on [2XBrowseBibliography[102X ([14XBrowse: BrowseBibliography[114X),
  see  the  documentation of this function for details, e.g., about the return
  value.[133X
  
  [33X[0;0YThe  returned record encodes the bibliography entries corresponding to those
  rows of the table that are [21Xclicked[121X in visual mode, in the same format as the
  return value of [2XParseBibXMLExtString[102X ([14XGAPDoc: ParseBibXMLextString[114X), see the
  manual of the [5XGAP[105X package [5XGAPDoc[105X [LN24] for details.[133X
  
  [33X[0;0Y[2XBrowseBibliographySporadicSimple[102X  can  be  called also via the menu shown by
  [2XBrowseGapData[102X ([14XBrowse: BrowseGapData[114X).[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27Xif IsBound( BrowseBibliographySporadicSimple ) then[127X[104X
    [4X[25X>[125X [27X  enter:= NCurses.keys.ENTER;;  nop:= [ 14, 14, 14 ];;[127X[104X
    [4X[25X>[125X [27X  BrowseData.SetReplay( Concatenation([127X[104X
    [4X[25X>[125X [27X    # choose the application[127X[104X
    [4X[25X>[125X [27X    "/Bibliography of Sporadic Simple Groups", [ enter, enter ],[127X[104X
    [4X[25X>[125X [27X    # search in the title column for the Atlas of Finite Groups[127X[104X
    [4X[25X>[125X [27X    "scr/Atlas of finite groups", [ enter,[127X[104X
    [4X[25X>[125X [27X    # and quit[127X[104X
    [4X[25X>[125X [27X    nop, nop, nop, nop ], "Q" ) );[127X[104X
    [4X[25X>[125X [27X  BrowseGapData();;[127X[104X
    [4X[25X>[125X [27X  BrowseData.SetReplay( false );[127X[104X
    [4X[25X>[125X [27Xfi;[127X[104X
  [4X[32X[104X
  
  [33X[0;0YThe  bibliographies  contained in the [5XATLAS[105X of Finite Groups [CCN+85] and in
  the [5XATLAS[105X of Brauer Characters [JLPW95] are available online in HTML format,
  see [7Xhttp://www.math.rwth-aachen.de/~Thomas.Breuer/atlasrep/bibl/index.html[107X.[133X
  
  [33X[0;0YThe    source    data    in    BibXMLext   format,   which   are   used   by
  [2XBrowseBibliographySporadicSimple[102X, are distributed with the [5XAtlasRep[105X package,
  in  four  files  with  suffix [11Xxml[111X in the package's [11Xbibl[111X directory. Note that
  each of the two books contains two bibliographies.[133X
  
  [33X[0;0YDetails  about  the BibXMLext format, including information how to transform
  the  data into other formats such as BibTeX, can be found in the [5XGAP[105X package
  [5XGAPDoc[105X (see [LN24]).[133X
  
