[1X1 Introduction to the [5XAtlasRep[1X Package[0X The aim of the [5XGAP[0m 4 package [5XAtlasRep[0m is to provide a link between [5XGAP[0m and the "[5XATLAS[0m of Group Representations", a database that comprises representations of many almost simple groups and information about their maximal subgroups. This database has been available independent of [5XGAP[0m at [7Xhttp://brauer.maths.qmul.ac.uk/Atlas[0m The [5XAtlasRep[0m package consists of this database (see Section [14X1.1[0m) and a [5XGAP[0m interface (see Section [14X1.2[0m); the latter is extended by further information available via the internet (see Section [14X1.3[0m). Information about installing and customizing the package can be found in the sections [14X1.4[0m, [14X1.5[0m, and [14X1.6[0m, [14X1.7[0m, [14X1.8[0m. Finally, Section [14X1.9[0m lists the changes w.r.t. previous releases of the package, and Section [14X1.10[0m acknowledges contributions of non-authors to the package. [1X1.1 An [5XATLAS[1X of Group Representations[0X The [5XATLAS[0m of Group Representations consists of matrices over various rings, permutations, and shell scripts encoding so-called black box programs (see [Nic06] and Section [14X4.2[0m). Many of these scripts are straight line programs (see [BSWW01], [SWW00], and [14X'Reference: Straight Line Programs'[0m) and straight line decisions (see Section [14X4.1[0m). These programs can be used to compute certain elements in a group G from its standard generators (see [Wil96] and [14X'Reference: Standard Generators of Groups'[0m), for example generators of maximal subgroups of G or representatives of conjugacy classes of G. The [5XATLAS[0m of Group Representations has been prepared by Robert Wilson, Peter Walsh, Jonathan Tripp, Ibrahim Suleiman, Richard Parker, Simon Norton, Simon Nickerson, Steve Linton, John Bray, and Rachel Abbott (in reverse alphabetical order). The information was computed and composed using computer algebra systems such as [5XMeatAxe[0m (see [Rin98]), Magma (see [CP96]), and [5XGAP[0m (in reverse alphabetical order). Part of the constructions have been documented in the literature on almost simple groups, or the results have been used in such publications, see for example the references in [CCNPW85] and [BN95]. If you use the [5XATLAS[0m of Group Representations to solve a problem then please send a short email to [7Xmailto:R.A.Wilson@qmul.ac.uk[0m about it. The [5XATLAS[0m of Group Representations database should be referenced with the entry [ATLAS] in the bibliography of this manual. If your work made use of functions of the [5XGAP[0m interface (see Section [14X1.2[0m) then you should also reference this interface, as follows. [4X--------------------------- Example ----------------------------[0X [4X@misc{ AtlasRep1.4,[0X [4X author = {Wilson, R. A. and Parker, R. A. and Nickerson, S. and[0X [4X Bray, J. N. and Breuer, T.},[0X [4X title = {{AtlasRep}, A \textsf{GAP} Interface to the Atlas of[0X [4X Group Representations,[0X [4X {V}ersion 1.4},[0X [4X month = {June},[0X [4X year = {2008},[0X [4X note = {Refereed \textsf{GAP} package},[0X [4X howpublished = {http://www.math.rwth-aachen.de/\~{}Thomas.Breuer/atlasrep}[0X [4X}[0X [4X------------------------------------------------------------------[0X For referencing the [5XGAP[0m system in general, use the entry [GAP] in the bibliography of this manual, see also [7Xhttp://www.gap-system.org[0m. [1X1.2 The GAP Interface to the [5XATLAS[1X of Group Representations[0X The [5XGAP[0m interface to the [5XATLAS[0m of Group Representations consists of essentially two parts. First, there is the [13Xuser interface[0m which allows the user to get an overview of the contents of the database, and to access the data in [5XGAP[0m format; this is described in Chapter [14X2[0m. Advanced users may add their own data to the database, this is described in Chapter [14X3[0m. Second, there is [13Xadministrational information[0m, which covers also the declaration of [5XGAP[0m objects such as straight line decisions and black box programs. This is important mainly for users interested in the actual implementation (e. g., for modifying the package) or in using it together with the [10XC[0m-[5XMeatAxe[0m standalone (see [Rin98]); this is described in Chapter [14X5[0m. Information concerning the [10XC[0m-[5XMeatAxe[0m, including the manual [Rin98], can be found at [7Xhttp://www.math.rwth-aachen.de/LDFM/homes/MTX[0m The [5XGAP[0m interface should be regarded as preliminary. Hopefully it will become more user-friendly when the [5XATLAS[0m of Group Representations will be integrated into a larger [5XGAP[0m database of groups and their representations, character tables, and tables of marks. The interface and this manual have been provided by Thomas Breuer, except for the interpreter for black box programs (see Section [14X4.2[0m), which is due to Simon Nickerson. Comments, bug reports, and hints for improving the interface can be sent to [7Xmailto:sam@math.rwth-aachen.de[0m. [1X1.3 Web Services for the [5XAtlasRep[1X Package[0X The home page of the [5XAtlasRep[0m package is [7Xhttp://www.math.rwth-aachen.de/~Thomas.Breuer/atlasrep[0m Besides package archives and introductory package information, it provides -- the current file with the [13Xtable of contents[0m (the file [11Xgap/atlasprm.g[0m of the package), cf. [2XReloadAtlasTableOfContents[0m ([14X1.6-1[0m), -- a [13Xstarter archive[0m containing many small representations and programs, -- the list of [13Xchanges of server files[0m in HTML format (cf. [2XAtlasOfGroupRepresentationsTestTableOfContentsRemoteUpdates[0m ([14X1.6-4[0m)), and -- an [13Xoverview of the data[0m available via the [5XGAP[0m interface to the [5XATLAS[0m of Group Representations, in HTML format; this is similar to the information shown by [2XDisplayAtlasInfo[0m ([14X2.5-1[0m); further information can be found on the home page of the [5XATLAS[0m (see the introduction to this chapter). [1X1.4 Installing the [5XAtlasRep[1X Package[0X To install the package, unpack the archive file in a directory in the [11Xpkg[0m directory of your local copy of [5XGAP[0m 4. This might be the [11Xpkg[0m directory of the [5XGAP[0m 4 root directory, see [14X'Reference: Installing a GAP Package'[0m for details. It is however also possible to keep an additional [11Xpkg[0m directory in your private directories, see Section [14X'Reference: GAP Root Directory'[0m. The latter possibility [13Xmust[0m be chosen if you do not have write access to the [5XGAP[0m root directory. Data files (in the subdirectories [11Xdatagens[0m and [11Xdataword[0m of the package) that are available from an earlier version of the package are in principle kept; see [2XAtlasOfGroupRepresentationsTestTableOfContentsRemoteUpdates[0m ([14X1.6-4[0m) for necessary updates. If it is likely that one will work offline, it makes sense to install the "starter archive" that can be downloaded from the package's homepage. The package consists entirely of [5XGAP[0m code, no external binaries need to be compiled for the package itself. However, if the [5XGAP[0m package [5XIO[0m [Neu07] is used to access remote data files (see Section [14X1.7-3[0m) then its external binary must be available. After unpacking the package archive, it should be checked whether the subdirectories [11Xdatagens[0m and [11Xdataword[0m of the package directory have write permissions for those users who will download files from the servers. The recommended permissions under UNIX are set as follows. [4X--------------------------- Example ----------------------------[0X [4Xyou@unix> chmod 1777 atlasrep/data*[0X [4Xyou@unix> ls -ld atlasrep/data*[0X [4Xdrwxrwxrwt 3 you you 1024 Oct 31 12:34 datagens[0X [4Xdrwxrwxrwt 3 you you 1024 Oct 31 12:34 dataword[0X [4X------------------------------------------------------------------[0X For checking the installation of the package, you should start [5XGAP[0m, load the package (see Section [14X1.5[0m), and then call [4X--------------------------- Example ----------------------------[0X [4Xgap> ReadPackage( "atlasrep", "tst/testinst.g" );[0X [4X------------------------------------------------------------------[0X If the installation is o.k. then the [5XGAP[0m prompt appears without anything else being printed; otherwise the output lines tell you what should be changed. More test files are available in the [11Xtst[0m directory of the package, see Section [14X5.8[0m for details. [11XPDF[0m and HTML versions of the package manual are available in the [11Xdoc[0m directory of the package. [1X1.5 Loading the [5XAtlasRep[1X Package[0X The [5XAtlasRep[0m package may be loaded automatically when [5XGAP[0m is started, for example when other [5XGAP[0m packages require it, or it has to be loaded within the [5XGAP[0m session as follows. [4X--------------------------- Example ----------------------------[0X [4Xgap> LoadPackage( "atlasrep" );[0X [4Xtrue[0X [4X------------------------------------------------------------------[0X See [14X'Reference: Loading a GAP Package'[0m for details about these alternatives. [1X1.6 Maintaining the Local Data of the [5XAtlasRep[1X Package[0X The current [13Xtable of contents[0m of the database is contained in the file [11Xgap/atlasprm.g[0m of the [5XAtlasRep[0m package. This file is read by default when the package is loaded. It may happen that new data files have been added to the servers since the last release of the [5XAtlasRep[0m package, thus it is useful to update the table of contents of the package from time to time. For that, one can fetch the most recent version of the file [11Xgap/atlasprm.g[0m from the home page of the package (see Section [14X1.3[0m), either by calling [2XReloadAtlasTableOfContents[0m ([14X1.6-1[0m) in a [5XGAP[0m session or "by hand". In the latter case, the new file can then be read into the [5XGAP[0m session via [2XReplaceAtlasTableOfContents[0m ([14X1.6-3[0m). Alternatively, one can add a line to the user's [11X.gaprc[0m file (see [14X'Reference: The .gaprc file'[0m), which assigns the filename of the current [11Xgap/atlasprm.g[0m file (as an absolute path or relative to the user's home directory, cf. [2XDirectory[0m ([14XReference: Directory[0m)) to the global variable [10XATLASREP_TOCFILE[0m; in this case, this file is read instead of the one from the package distribution when the package is loaded. Users who have write access to the directory where the [5XAtlasRep[0m package is installed can alternatively use the [11Xmaketoc[0m script in the [11Xetc[0m directory of the package for regularly updating the file [11Xgap/atlasprm.g[0m. Users without this write access can store the new file in a different place, and read it with [2XReplaceAtlasTableOfContents[0m ([14X1.6-3[0m). [1X1.6-1 ReloadAtlasTableOfContents[0m [2X> ReloadAtlasTableOfContents( [0X[3Xdirname[0X[2X ) ____________________________[0Xfunction [6XReturns:[0X [9Xfail[0m if the required table of contents could not be reloaded, otherwise [9Xtrue[0m. Let [3Xdirname[0m be a string, which must be one of [10X"remote"[0m, [10X"local"[0m, or the name of a private data directory (see Chapter [14X3[0m). In the case of [10X"remote"[0m, the file [10Xatlasprm.g[0m is fetched from the package's home page, and then read into [5XGAP[0m. In the case of [10X"local"[0m, the subset of the data listed in the [10X"remote"[0m table of contents is considered that are actually available in the local data directories. In the case of a private directory, its contents is inspected, and the table of contents for [3Xdirname[0m is replaced by the one obtained from inspecting the actual contents of the data directories (see Section [14X5.7[0m). [1X1.6-2 StoreAtlasTableOfContents[0m [2X> StoreAtlasTableOfContents( [0X[3Xfilename[0X[2X ) ____________________________[0Xfunction Let [3Xfilename[0m be a string. This function prints the loaded table of contents of the servers to the file with name [3Xfilename[0m. [1X1.6-3 ReplaceAtlasTableOfContents[0m [2X> ReplaceAtlasTableOfContents( [0X[3Xfilename[0X[2X ) __________________________[0Xfunction Let [3Xfilename[0m be the name of a file that has been created with [2XStoreAtlasTableOfContents[0m ([14X1.6-2[0m). [2XReplaceAtlasTableOfContents[0m first removes the information that [5XGAP[0m has stored about the table of contents of the servers, and then reads the file with name [3Xfilename[0m, thus replacing the previous information by the stored one. [1X1.6-4 AtlasOfGroupRepresentationsTestTableOfContentsRemoteUpdates[0m [2X> AtlasOfGroupRepresentationsTestTableOfContentsRemoteUpdates( [0X[3X[0X[2X ) __[0Xfunction [6XReturns:[0X the list of names of all locally available data files that should be removed. This function fetches the file [11Xchanges.html[0m from the package's home page, extracts the times of changes for the data files in question, and compares them with the times of the last changes of the local data files. For that, the [5XGAP[0m package [5XIO[0m [Neu07] is needed; if it is not available then an error message is printed, and [9Xfail[0m is returned. If the time of the last modification of a server file is later than that of the local copy then the local file must be updated. (This means that [10Xtouch[0ming files in the local directories will cheat this function.) It is useful that a system administrator (i. e., someone who has the permission to remove files from the data directories) runs this function from time to time, and afterwards removes the files in the list that is returned. This way, new versions of these files will be fetched automatically from the servers when a user asks for their data. [1X1.7 User Parameters for the [5XAtlasRep[1X Package[0X This section lists global parameters for which it might make sense to change their defaults by assignments to global variables, either just for the current [5XGAP[0m session or as user preferences in the user's [11X.gaprc[0m file (see [14X'Reference: The .gaprc file'[0m). [1X1.7-1 Local or Remote Access[0X There are two possibilities to use the [5XAtlasRep[0m package. [8X[13XLocal access only (offline)[0m[8X[0m You can restrict he access to the data that are actually stored in the local installation of [5XGAP[0m. [8X[13XRemote access (online)[0m[8X[0m If your computer is connected to a network that provides access to the [5XATLAS[0m data (for example the internet) then the functions of the package may fetch the requested data automatically from remote servers when they are required for the first time; these data are then by default stored in the local copy, so later access to them needs no network transfer. The latter possibility is presently not used by other [5XGAP[0m packages, so it may be regarded as an important feature of the [5XAtlasRep[0m package. Anyhow it requires a few words of explanation. The possibility of online access reflects in particular the fact that the [5XATLAS[0m of Group Representations is designed as an [13Xopen database[0m, it is expected to grow. As soon as the developers of the [5XATLAS[0m of Group Representations add new information to the servers, these data become available in [5XGAP[0m when remote access is enabled, after one has updated the corresponding table of contents (see Section [14X1.6[0m). Remote access is enabled if and only if the value of the [10Xremote[0m component of the global variable [2XAtlasOfGroupRepresentationsInfo[0m ([14X5.1-5[0m) is [9Xtrue[0m. If one wants to work offline, i.e., if one does [13Xnot[0m want [5XGAP[0m to attempt accessing remote data then this value must be set to [9Xfalse[0m. Conversely, if the default value of the [10Xremote[0m component in your [5XGAP[0m installation is [9Xfalse[0m then changing this value to [9Xtrue[0m may be not successful. First, it might be the case that no server is reachable. And second, if one can in principle [13Xdownload[0m files from a server then it might be impossible to actually [13Xstore[0m these files in the data directories of the installed package; in this case, it is advisable to install the whole package or just its data directories in a private directory, see [14X'Reference: GAP Root Directory'[0m for details. [1X1.7-2 Adding and Removing Servers[0X When access to remote data is enabled (see Section [14X1.7-1[0m) then the available servers are given by the [10Xservers[0m component of the global variable [2XAtlasOfGroupRepresentationsInfo[0m ([14X5.1-5[0m). [13XRemoving[0m entries from this list means to disable access to the corresponding servers, [13Xadding[0m entries makes the corresponding servers available. Of course the latter makes sense only if the new servers really exist, for example in a local network. Currently there is just one remote server. As soon as other servers become available, or a server name is changed which makes it necessary to adjust the [10Xservers[0m component, this will be announced in the [5XGAP[0m Forum, cf. [14X'Tutorial: Further Information about GAP'[0m. The same holds when upgrades of the package become available. [1X1.7-3 Accessing Data Files with the [5XGAP[1X Package [5XIO[1X or with [11Xwget[1X[0X When access to remote data is enabled (see Section [14X1.7-1[0m) then one needs either the [5XGAP[0m package [5XIO[0m [Neu07] or the external program [11Xwget[0m for accessing data files. The chosen alternative is given by the value of the [10Xwget[0m component of the global variable [2XAtlasOfGroupRepresentationsInfo[0m ([14X5.1-5[0m). If this component has the value [9Xtrue[0m then only [11Xwget[0m is tried, if the value is [9Xfalse[0m then only the [5XIO[0m package is used. If this component is not bound or bound to another value than [9Xtrue[0m or [9Xfalse[0m (this is also the default) then the [5XIO[0m package is preferred to [11Xwget[0m if this package is available, and otherwise [11Xwget[0m is tried. Note that the system program [11Xwget[0m may be not available, and that it may require some work to install it; hints for that can be found on the home page of the [5XAtlasRep[0m package (see Section [14X1.3[0m). [1X1.7-4 Compressed or Uncompressed Data Files[0X When used with UNIX, [5XGAP[0m can read [11Xgzip[0mped files, see [14X'Reference: Saving and Loading a Workspace'[0m. If the component [10Xcompress[0m of [2XAtlasOfGroupRepresentationsInfo[0m ([14X5.1-5[0m) has the value [9Xtrue[0m then each [5XMeatAxe[0m format file that is fetched from a remote server is afterwards compressed with [11Xgzip[0m. This saves a lot of space if many [5XMeatAxe[0m format files are accessed. (Note that data files in other formats are very small.) For example, at the time of the release of version 1.4 there were about 8400 data files in [5XMeatAxe[0m format, which needed about 1400 MB in uncompressed text format and about 275 MB in compressed text format. The default value for the component [10Xcompress[0m is [9Xfalse[0m. [1X1.7-5 Customizing [10XDisplayAtlasInfo[1X[0X The way how [2XDisplayAtlasInfo[0m ([14X2.5-1[0m) shows the requested overview is controlled by the component [10XdisplayFunction[0m of [2XAtlasOfGroupRepresentationsInfo[0m ([14X5.1-5[0m). The default value is [2XPrint[0m ([14XReference: Print[0m), another useful value is [2XPager[0m ([14XReference: Pager[0m). [1X1.7-6 Customizing the Access to Data Files[0X By default, local data files are stored in the subdirectories [11Xdatagens[0m and [11Xdataword[0m of the package, and the files are exactly the text files provided on the servers. However, a more flexible approach may be useful. First, one may want to use [13Xdifferent file formats[0m, for example the [5XMeatAxe[0m binary files that are provided by the servers parallel to the [5XMeatAxe[0m text files. Second, one may want to use [13Xa different directory structure[0m, for example the same structure as used on the servers âthis makes sense for example if a local mirror of a server is available, because then one can read the server files directly, without transferring/copying them to another directory. As a consequence, one would like to customize the meaning of the following three access steps. [8XAre the required filed locally available?[0m The required files may have a different name or a different path, and the data can be available in one file or can be distributed to several files. [8XHow can a file be made locally available?[0m A different server file may be fetched or some postprocessing may be required. [8XHow is the data of a file accessed by [5XGAP[0m[8X?[0m A different function may be needed to read the file. Details how to achieve this can be found in Section [14X5.2[0m. [1X1.7-7 Reading Large Matrices over Finite Fields[0X Matrices over finite fields in [5XGAP[0m can be represented in a compressed format that needs less space than the corresponding text file. Such a [5XMeatAxe[0m format text file can be read by [2XScanMeatAxeFile[0m ([14X5.3-1[0m) either line by line (which is the default) or as a whole; the latter is faster but needs more space than the former. For example, a 4370 by 4370 matrix over the field with two elements (as occurs for an irreducible representation of the Baby Monster) requires less than 3 MB space in [5XGAP[0m but the corresponding [5XMeatAxe[0m format text file is more than 19 MB large, which means that when one reads the file with the fast variant, [5XGAP[0m will temporarily grow by more than this value. One can change the mode by setting the global variable [2XCMeatAxe.FastRead[0m ([14X5.1-4[0m) to [9Xtrue[0m or [9Xfalse[0m, respectively. Note that this parameter is meaningful only when [2XScanMeatAxeFile[0m ([14X5.3-1[0m) is used. It has no effect for example if [5XMeatAxe[0m binary files are read, cf. [2XFFMatOrPermCMtxBinary[0m ([14X5.3-5[0m). [1X1.7-8 AtlasOfGroupRepresentationsShowUserParameters[0m [2X> AtlasOfGroupRepresentationsShowUserParameters( [0X[3X[0X[2X ) ________________[0Xfunction This function prints an overview of the current values of the user parameters introduced in this section. [1X1.8 Extending the [5XATLAS[1X Database[0X Users who have computed new representations that might be interesting for inclusion into the [5XATLAS[0m of Group representations can send the data in question to [7Xmailto:R.A.Wilson@qmul.ac.uk[0m. It is also possible to store "private" representations and programs in local directories, and to use them in the same way as the "official" data. See Chapter [14X3[0m for details. [1X1.9 What's New in [5XAtlasRep[1X, Compared to Older Versions?[0X [1X1.9-1 What's New in Version 1.4?[0X -- In addition to the group orders that were added in version 1.3 (see Section [14X1.9-3[0m), also many orders of maximal subgroups are now available. These values occur in the records returned by [2XAtlasProgram[0m ([14X2.5-3[0m) (for the case of [10X"maxes"[0m type programs) and of the three argument version of [2XAtlasGenerators[0m ([14X2.5-2[0m); now a [10Xsize[0m component may be bound. In these cases, the groups returned by [2XAtlasSubgroup[0m ([14X2.5-7[0m) have the [2XSize[0m ([14XReference: Size[0m) attribute set. For this feature, the function [2XAGRGNAN[0m ([14X5.7-1[0m) was generalized, the function [2XAtlasOfGroupRepresentationsTestWords[0m ([14X5.8-6[0m) was improved for [10X"maxes"[0m type programs, and the function [2XAtlasOfGroupRepresentationsTestSubgroupOrders[0m ([14X5.8-2[0m) for preparing the values was added; this function serves also as a consistency check. -- The information about the number of maximal subgroups, if available, is now used in [2XDisplayAtlasInfo[0m ([14X2.5-1[0m). -- In many cases, straight line programs for computing generators of maximal subgroups of a group G, say, can in fact be used to compute also generators of maximal subgroups of downward extensions of G; if not then it may suffice to extend the given straight line programs by additional generators, see [2XAtlasOfGroupRepresentationsTestCompatibleMaxes[0m ([14X5.8-4[0m). Currently this yields more than 200 more possibilities to compute maximal subgroups, this means a growth by about 25 percent. For example, all maximal subgroups of 12.M_22 and 2.Fi_22 can now be accessed via [2XAtlasGenerators[0m ([14X2.5-2[0m). (Of course this extension means only that one can access the straight line programs in question automatically via the [5XGAP[0m interface. In principle one could have used them already before, by explicitly applying a straight line program for a factor group to generators of a group, and perhaps adding some element in the kernel of the natural epimorphism.) For this feature, information about the compatibility of standard generators of groups and their factor groups was added, see [2XAtlasOfGroupRepresentationsTestStdCompatibility[0m ([14X5.8-3[0m). -- The bibliographies contained in the [5XATLAS[0m of Finite Groups [CCNPW85] and in the [5XATLAS[0m of Brauer Characters [JLPW95] are now available, see Section [14X4.4[0m. -- If the [5XGAP[0m package [5XBrowse[0m (see [BL08]) is loaded then the new functions [2XBrowseMinimalDegrees[0m ([14X4.3-6[0m) and [2XBrowseBibliographySporadicSimple[0m ([14X4.4-1[0m) are available; these functions can be called also by choosing the corresponding menu entries of the [5XBrowse[0m application [2XBrowseGapData[0m ([14XBrowse: BrowseGapData[0m). -- The function [2XAtlasGroup[0m ([14X2.5-6[0m) now admits also the return value of [2XOneAtlasGeneratingSetInfo[0m ([14X2.5-4[0m) as its argument. [1X1.9-2 What's New in Version 1.3.1?[0X This version was mainly released in order to fix a few problems. Now one does not get warnings about unbound variables when the package is loaded and the [5XGAP[0m package [5XIO[0m [Neu07] is not available, and pathological situations in [2XFFMatOrPermCMtxBinary[0m ([14X5.3-5[0m) (concerning extremely short corrupted data files and different byte orderings in binary files) are handled more carefully. Besides this, the two functions [2XAtlasGroup[0m ([14X2.5-6[0m) and [2XAtlasSubgroup[0m ([14X2.5-7[0m) were introduced, and the extended function [2XQuaternionAlgebra[0m ([14XReference: QuaternionAlgebra[0m) of [5XGAP[0m 4.4.10 can now be used for describing base rings in [2XOneAtlasGeneratingSetInfo[0m ([14X2.5-4[0m) and [2XAllAtlasGeneratingSetInfos[0m ([14X2.5-5[0m). (This is the reason why this version of the package requires at least version 4.4.10 of [5XGAP[0m.) [1X1.9-3 What's New in Version 1.3?[0X -- The database was extended, see Section [14X1.7-4[0m for the number and size of files. -- New data types and corresponding [5XGAP[0m objects have been introduced, for representing semi-presentations, presentations, and programs for finding standard generators. For details, see [2XAtlasProgram[0m ([14X2.5-3[0m), Chapter [14X4[0m, and Section [14X5.6[0m. -- The records returned by the functions [2XAtlasGenerators[0m ([14X2.5-2[0m), [2XOneAtlasGeneratingSetInfo[0m ([14X2.5-4[0m), and [2XAllAtlasGeneratingSetInfos[0m ([14X2.5-5[0m) now contain the name and (if known) the order of the group in question, and also components describing the degree in the case of permutation representations or the dimension and the base ring of the natural module in the case of matrix representations. -- For many of the groups, information about the minimal degree of faithful permutation representations and the minimal dimensions of faithful matrix representations in various characteristics is available for [2XDisplayAtlasInfo[0m ([14X2.5-1[0m), [2XOneAtlasGeneratingSetInfo[0m ([14X2.5-4[0m), and [2XAllAtlasGeneratingSetInfos[0m ([14X2.5-5[0m), see also Section [14X4.3[0m. For these functions, also properties such as [2XIsPrimeInt[0m ([14XReference: IsPrimeInt[0m) can be used to describe the intended restriction of the output. -- One can now use [2XPager[0m ([14XReference: Pager[0m) in [2XDisplayAtlasInfo[0m ([14X2.5-1[0m), see Section [14X1.7-5[0m. An interactive alternative to [2XDisplayAtlasInfo[0m ([14X2.5-1[0m) is provided by the function [2XBrowseAtlasInfo[0m ([14XBrowse: BrowseAtlasInfo[0m) from the new (recommended) [5XGAP[0m package [5XBrowse[0m [BL08]. -- The functions [2XOneAtlasGeneratingSetInfo[0m ([14X2.5-4[0m) and [2XAllAtlasGeneratingSetInfos[0m ([14X2.5-5[0m) now admit also a list of group names as the first argument. -- The functions for actually accessing the data are more flexible now, see Section [14X1.7-6[0m. -- For transferring remote data, the [5XGAP[0m package [5XIO[0m [Neu07] can now be used (and is recommended) as an alternative to [11Xwget[0m, see Section [14X1.7-3[0m. -- The address of the data server has changed. Since the access to the server is no longer possible via [11Xftp[0m, the mechanim used up to version 1.2, which was based on [11Xftp[0m, had to be rewritten. The main consequence of this change is that information about updates of the table of contents is now provided at the package's homepage. This means that on the one hand, now package users cannot [13Xcompute[0m the table of contents directly from the server data, but on the other hand the update information can be [13Xdownloaded[0m without the necessity to install [11Xperl[0m. Another consequence is that the system program [11Xls[0m is no longer needed, see Section [14X1.9-5[0m. -- The package manual has been restructured, extended and improved. It is now based on the package [5XGAPDoc[0m [LN08]. [1X1.9-4 What's New in Version 1.2?[0X Not much. The release of Version 1.2 became necessary first of all in order to provide a package version that is compatible with [5XGAP[0m 4.4, since some cross-references into the [5XGAP[0m Reference Manual were broken due to changes of section names. Additionally, several web addresses concerning the package itself were changed and thus had to be adjusted. This opportunity was used -- to upgrade the administrational part for loading the package to the mechanism that is recommended for [5XGAP[0m 4.4, -- to extend the test suite, which now covers more consistency checks using the [5XGAP[0m Character Table Library [Bre04], -- to make the function [2XScanMeatAxeFile[0m ([14X5.3-1[0m) more robust, due to the fact that the [5XGAP[0m function [2XPermList[0m ([14XReference: PermList[0m) now returns [9Xfail[0m instead of raising an error, -- to change the way how representations with prescribed properties are accessed (the new function [2XOneAtlasGeneratingSetInfo[0m ([14X2.5-4[0m) is now preferred to the former [10XOneAtlasGeneratingSet[0m, and [2XAllAtlasGeneratingSetInfos[0m ([14X2.5-5[0m) has been added in order to provide programmatic access in parallel to the human readable descriptions printed by [2XDisplayAtlasInfo[0m ([14X2.5-1[0m)), -- and last but not least to include the current table of contents of the underlying database. For [5XAtlasRep[0m users, the new feature of [5XGAP[0m 4.4 is particularly interesting that due to better kernel support, reading large matrices over finite fields is now faster than it was in [5XGAP[0m 4.3. [1X1.9-5 What's New in Version 1.1?[0X The biggest change w.r.t. Version 1.1 is the addition of private extensions (see Chapter [14X3[0m). It includes a new "free format" for straight line programs (see Section [14X3.2[0m). Unfortunately, this feature requires the system program [11Xls[0m, so it may be not available for example under MS Windows operating systems. [But see Section [14X1.9-3[0m.] In order to admit the addition of other types of data, the implementation of several functions has been changed. Data types are described in Section [14X5.5[0m. An example of a new data type are quaternionic representations (see Section [14X5.6[0m). The user interface itself (see Chapter [14X2[0m) remained the same. As an alternative to [10Xperl[0m, one can use [10Xwget[0m now for transferring data files (see [14X1.7[0m). Data files can be read much more efficiently in [5XGAP[0m 4.3 than in [5XGAP[0m 4.2. In Version 1.1 of the [5XAtlasRep[0m package, this feature is used for reading matrices and permutations in [5XMeatAxe[0m text format with [2XScanMeatAxeFile[0m ([14X5.3-1[0m). As a consequence, (at least) [5XGAP[0m 4.3 is required for [5XAtlasRep[0m Version 1.1. The new [10Xcompress[0m component of the global variable [2XAtlasOfGroupRepresentationsInfo[0m ([14X5.1-5[0m) allows one to store data files automatically in [11Xgzip[0mped form. For matrix representations in characteristic zero, invariant forms and generators for the centralizer algebra are now accessible in [5XGAP[0m if they are contained in the source files --this information had been ignored in Version 1.0 (see [2XAtlasOfGroupRepresentationsTestTableOfContentsRemoteUpdates[0m ([14X1.6-4[0m) for necessary updates). Additional information is now available via the internet (see [14X1.3[0m). The update facilities have been extended (see [14X1.6[0m). The manual is now distributed also in pdf and HTML format; on the other hand, the PostScript format manual is no longer contained in the archives. Apart from these changes, a few minor bugs in the handling of [5XMeatAxe[0m files have been fixed, typos in the documentation have been corrected, and the syntax checks for [5XATLAS[0m straight line programs (see [14X5.4[0m) have been improved. [1X1.10 Acknowledgments[0X The perl script that had been used for fetching remote data until version 1.2 had been kindly provided by Frank Lübeck and Max Neunhöffer. Thanks also to Greg Gamble and Alexander Hulpke for technical hints concerning "standard" perl. Ulrich Kaiser helped with preparing the package for MS Windows. The idea to support private extensions of the package (see Chapter [14X3[0m) is due to Klaus Lux. He used a preliminary version of [5XAtlasRep[0m Version 1.1, and helped to fix several bugs. The functions [2XCMtxBinaryFFMatOrPerm[0m ([14X5.3-4[0m) and [2XFFMatOrPermCMtxBinary[0m ([14X5.3-5[0m) were contributed by Frank Lübeck. The [5XGAPDoc[0m package [LN08], which is used for processing the package manual, was written by Frank Lübeck and Max Neunhöffer. The [5XGAP[0m package [5XIO[0m [Neu07], which is recommended for transferring data, was written by Max Neunhöffer. Max has also suggested the generalization of the data access described in Section [14X1.7-6[0m. Gunter Malle had suggested to make the information about representations of minimal degree accessible.