The aim of the GAP 4 package AtlasRep is to provide a link between GAP and the ``ATLAS 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 GAP at http://www.mat.bham.ac.uk/atlas
The AtlasRep package consists of this database and a GAP interface.
1.1 An Atlas of Group Representations
The Atlas of Group Representations consists of matrices over various rings, permutations, and shell scripts encoding so-called straight line programs (see BSW01, SWW00, and Straight Line Programs in the GAP Reference Manual). These programs can be used to compute certain elements in a group G from its standard generators (see Wil96 and Standard Generators of Groups in the GAP Reference Manual) of G, for example generators of maximal subgroups of G or representatives of conjugacy classes of G.
The ATLAS of Group Representations has been prepared by Robert Wilson, Peter Walsh, Jonathan Tripp, Ibrahim Suleiman, Stephen Rogers, Richard Parker, Simon Norton, Steve Linton, and John Bray (in reverse alphabetical order).
The information was computed and composed using computer algebra systems such as MeatAxe (see Rin98), Magma (see CP96), and GAP (in reverse alphabetical order). Part of the constructions have been documented in the literature on almost simple groups, or the results have been used in such publications, see for example the references in CCN85 and BN95.
If you use the ATLAS of Group Representations to solve a problem then please send a short email to R.A.Wilson@bham.ac.uk about it. The ATLAS of Group Representations database should be referenced with the entry AGR in the bibliography of this manual.
If your work made use of functions of the GAP interface (see The GAP Interface to the Atlas of Group Representations) then you should also reference this interface, via the entry Bre01 in the bibliography of this manual.
For referencing the GAP system in general, use the entry GAP4 in the bibliography of this manual.
1.2 The GAP Interface to the Atlas of Group Representations
The GAP interface to the ATLAS of Group Representations consists of essentially two parts. First, there is the user interface which allows the user to get an overview of the contents of the database, and to access the data in GAP format; this is described in Chapter The User Interface of the AtlasRep Package. Second, there is administrational information which is important only for users interested in the actual implementation (e. g., for modifying the package) or in using it together with the C-MeatAxeindexC-MeatAxe standalone (see Rin98); this is described in Chapter Technicalities of the AtlasRep Package.
Information concerning the C-MeatAxe, including the manual Rin98, can be found at http://www.math.rwth-aachen.de/LDFM/homes/MTX
A GAP 4 Package that provides access to the functionality of the C-MeatAxe is in preparation.
The GAP interface should be regarded as preliminary. Hopefully it will become more user-friendly when the ATLAS of Group Representations will be integrated into a larger GAP database of groups and their representations, character tables, and tables of marks.
The interface and this manual have been provided by Thomas Breuer. Comments, bug reports, and hints for improving the interface can be sent to sam@math.rwth-aachen.de.
1.3 Local or Remote Installation of the AtlasRep Package
There are two possibilities to install the AtlasRep package.
The latter possibility is presently not used by other GAP packages, so it may be regarded as an important feature of the AtlasRep package. Anyhow it requires a few sentences of explanation.
The possibility of a remote installation reflects in particular the fact that the ATLAS of Group Representations is designed as an open database, it is expected to grow. As soon as the developers of the ATLAS of Group Representations add new information to the servers, these data become available in remote installations of the package after updating the corresponding table of contents (see Updating the Tables of Contents of the AtlasRep Package).
Currently there is just one remote server. As soon as new servers become available, or a server name is changed (see Global Variables Used by the AtlasRep Package), which makes it necessary to adjust the installation of the AtlasRep package, this will be announced in the GAP Forum (see Further Information about GAP in the GAP Tutorial). The same holds when upgrades of the package become available. Additionally, the GAP servers will provide this information.
1.4 Installing the AtlasRep Package
To install the AtlasRep package unpack the archive file in a
directory in the pkg directory of your local copy of GAP 4.
This might be the pkg directory of the GAP 4 home directory,
see Section Installing GAP Packages
of the GAP 4 Reference Manual for details.
It is however also possible to keep an additional pkg directory
in your private directories,
see Installing a GAP Package in your home directory
of the GAP 4 Reference Manual.
The latter possibility must be chosen if you do not have write access
to the GAP root directory.
The package consists entirely of GAP code plus a few scripts,
no external binaries need to be compiled.
If one wants to use the remote installation of the package
(see Local or Remote Installation of the AtlasRep Package),
one needs the perl module libnet;
most Linux distributions provide it via add-ons.
(The module is called libnet-perl in Debian Linux and perl-libnet in
RedHat Linux.)
In the case that the libnet module is missing on your machine,
use man perlmodinstall for information on how to install it;
if you have to adjust the environment variable PERLLIB,
call man perlrun for details.
After unpacking the archive, it should be checked whether the subdirectories
datagens and dataword of the atlasrep directory have write permissions
for those users who will download files from the servers.
The recommended permissions under UNIX are set as follows.
you@unix> chmod 1777 atlasrep/data* you@unix> ls -ld atlasrep/data* drwxrwxrwt 3 you you 1024 Mar 22 12:34 datagens drwxrwxrwt 3 you you 1024 Mar 22 12:34 dataword
Both dvi and PostScript versions of the AtlasRep manual are available
(as manual.dvi and manual.ps respectively) in the doc directory
of the home directory of AtlasRep,
an HTML version can be found in the htm directory.
1.5 More About Installing the AtlasRep Package
When GAP uses the feature to access files on remote servers,
it calls the system programs perl, awk, ftp, and ls;
the relevant scripts can be found in the etc directory of the package.
This works under UNIX, but may cause problems when used with other
operating systems.
For example, in principle the system programs needed are available for
MS-Windows, but it may require some work to install them.
A further change may be useful if in principle there is a network connection
to a remote server but GAP shall not attempt to access remote data.
In this case, the value of the remote component of the global variable
AtlasOfGroupRepresentationsInfo (see AtlasOfGroupRepresentationsInfo)
should be set from the default true to false;
this variable is set in the file types.g in the gap directory of the
package.
Independent of the default value of AtlasOfGroupRepresentationsInfo
(see AtlasOfGroupRepresentationsInfo),
each user can individually change the remote and servers components
of this record, for example using a .gaprc file
(see The .gaprc file in the GAP Reference Manual).
Note that if in the GAP installation, the remote value is set to false
then it might be impossible to actually store files fetched from a remote
server in the data directories of the installed package;
in such cases, it is advisable for the user in question to install the
package or just its data directories in a private directory,
see Installing a GAP Package in your home directory in the GAP
Reference Manual for details.
Removing entries from the servers list means to disable access to the
corresponding servers.
Adding entries makes of course sense only if corresponding servers really
exist, for example in a local network.
Under UNIX, GAP can read gzipped files
(see Saving and Loading a Workspace in the GAP Reference Manual).
If the component compress of AtlsOfGroupRepresentationsInfo has the
value true then each MeatAxe format file that is fetched from a remote
server is afterwards compressed with gzip.
This saves a lot of space if many MeatAxe format files are accessed.
(Note that data files in other formats are very small.)
For example, at the time of the release of version 1.1 there were about
5 800 data files in MeatAxe format, which needed 1 085 MB in
uncompressed and about 180 MB in compressed form.
The default value for the component compress is false.
For checking the installation, one can run the tests in the files
atlasrep.tst and docxpl.tst in the tst directory of the package
(see Sanity Checks for the Atlas of Group Representations for details).
1.6 Maintaining the Local Data of the AtlasRep Package
It may be useful if a system administrator runs the following function from time to time, and then removes the files listed in the printed messages.
AtlasOfGroupRepresentationsTestTableOfContentsRemoteUpdates( ) F
It is checked whether files in the local data directories must be updated because of changes of the corresponding files in the remote data directories. (Such changes are restricted to bugfixes, their number is expected to be very small.)
For each local file that must be updated, a line of the following form is printed.
#I update local file `...'
The necessity of updating a file is detected from the fact that the time
of its last modification on the server is later than that of the local
copy.
(This means that touching files in the local directories will cheat
this function.)
1.7 Loading the AtlasRep Package
The AtlasRep package may be loaded automatically when GAP is started, or it has to be loaded within GAP as follows.
gap> RequirePackage( "atlasrep" );See Loading a GAP Package in the GAP Reference Manual for details about these alternatives.
1.8 Extending the Atlas Database
Users who have computed new representations that might be interesting for inclusion into the ATLAS of Group representations can send the data in question to R.A.Wilson@bham.ac.uk.
It is also possible to store ``private'' representations and straight line programs in local directories, and to use them in the same way as the ``official'' data. See Chapter Private Extensions of the AtlasRep Package for details.
1.9 What's New in Version 1.1?
The biggest change w.r.t. Version 1.1 is the addition of private extensions (see Chapter Private Extensions of the AtlasRep Package). It includes a new ``free format'' for straight line programs (see The Effect of Private Extensions on the User Interface).
In order to admit the addition of other types of data, the syntax for the access to straight line programs representing outer automorphisms has been changed --in this respect, the new version is not compatible with Version 1.0!
Except for the above inconsistency, the user interface remained the same. Nevertheless, the GAP code has been completely rewritten.
Data files can be read much more efficiently in GAP 4.3 than in GAP 4.2. In Version 1.1 of the AtlasRep package, this feature is used for reading permutations in MeatAxe text format. (One can use this version of the package also with GAP 4.2.)
Apart from these changes, a few minor bugs in the handling of MeatAxe files have been fixed, and the syntax checks for ATLAS straight line programs (see Reading and Writing Atlas Straight Line Programs) have been improved.
The perl script for fetching remote data has been kindly provided by Frank Lübeck and Max Neunhöffer. Thanks also to Greg Gamble and Alexander Hulpke for technical hints concerning ``standard'' perl.
The idea of supporting private extensions of the package (see Chapter Private Extensions of the AtlasRep Package) is due to Klaus Lux. He used a preliminary version of AtlasRep Version 1.1, and helped to fix several bugs.
AtlasRep manual