chap1.txt

  
  1 Preface
  
  Welcome  to  GAP. This preface serves not only to introduce this manual, the
  GAP Tutorial, but also as an introduction to the system as a whole.
  
  GAP  stands  for  Groups, Algorithms and Programming. The name was chosen to
  reflect  the aim of the system, which is introduced in this tutorial manual.
  Since that choice, the system has become somewhat broader, and you will also
  find  information  about  algorithms  and  programming  for  other algebraic
  structures, such as semigroups and algebras.
  
  In  addition  to  this  manual, there is the GAP Reference Manual containing
  detailed  documentation  of  the  mathematical functionality of GAP, and the
  manual  called  GAP  -  Changes  from  Earlier Versions which describes most
  essential changes from previous GAP releases.
  
  A  lot  of  the  functionality  of  the  system  and a number of contributed
  extensions  are  provided  as  GAP  packages  and  each of these has its own
  manual.
  
  Subsequent  sections of this preface explain the structure of the system and
  list sources of further information about GAP.
  
  
  1.1 The GAP System
  
  GAP  is  a  free,  open  and  extensible software package for computation in
  discrete  abstract  algebra. The terms free and open describe the conditions
  under  which  the  system  is  distributed -- in brief, it is free of charge
  (except  possibly  for the immediate costs of delivering it to you), you are
  free  to  pass  it  on within certain limits, and all of the workings of the
  system  are  open for you to examine and change. Details of these conditions
  can be found in Section 'Reference: Copyright and License'.
  
  The  system is extensible in that you can write your own programs in the GAP
  language,  and use them in just the same way as the programs which form part
  of  the  system (the library). Indeed, we actively support the contribution,
  refereeing  and distribution of extensions to the system, in the form of GAP
  packages.  Further details of this can be found in chapter 'Reference: Using
  GAP Packages', and on our website.
  
  Development  of  GAP began at Lehrstuhl D für Mathematik, RWTH-Aachen, under
  the leadership of Joachim Neubüser in 1985. Version 2.4 was released in 1988
  and  version  3.1 in 1992. In 1997 coordination of GAP development, now very
  much  an  international  effort,  was  transferred to St Andrews. A complete
  internal  redesign  and  almost complete rewrite of the system was completed
  over  the  following years and version 4.1 was released in July 1999. A sign
  of  the  further internationalization of the project was the GAP 4.4 release
  in  2004,  which  has  been coordinated from Colorado State University, Fort
  Collins.
  
  More  information  on  the motivation and development of GAP to date, can be
  found on our Web pages in a section entitled Release history and Prefaces.
  
  For  those  readers  who have used an earlier version of GAP, an overview of
  the  changes  from  GAP 4.4  and  a  brief  summary  of changes from earlier
  versions is given in a separate manual 'Changes: Changes between GAP 4.4 and
  GAP 4.5'.
  
  The  system  that you are getting now consists of a core system and a number
  of packages. The core system consists of four main parts.
  
  1   A kernel, written in C, which provides the user with
  
            automatic  dynamic  storage  management,  which the user needn't
              bother about in his programming;
  
            a   set  of  time-critical  basic  functions,  e.g.  arithmetic,
              operations  for integers, finite fields, permutations and words,
              as well as natural operations for lists and records;
  
            an  interpreter  for  the  GAP  language,  an untyped imperative
              programming  language  with functions as first class objects and
              some  extra  built-in data types such as permutations and finite
              field  elements. The language supports a form of object-oriented
              programming, similar to that supported by languages like C++ and
              Java but with some important differences.
  
            a  small  set of system functions allowing the GAP programmer to
              handle  files  and  execute  external programs in a uniform way,
              regardless of the particular operating system in use.
  
            a  set  of  programming tools for testing, debugging, and timing
              algorithms.
  
            a read-eval-view style user interface.
  
  2   A  much  larger  library of GAP functions that implement algebraic and
        other  algorithms. Since this is written entirely in the GAP language,
        the GAP language is both the main implementation language and the user
        language  of  the  system.  Therefore  the  user  can as easily as the
        original  programmers  investigate  and vary algorithms of the library
        and  add  new  ones  to  it,  first for own use and eventually for the
        benefit of all GAP users.
  
  3   A  library  of group theoretical data which contains various libraries
        of  groups,  including  the  library  of  small groups (containing all
        groups  of order at most 2000, except those of order 1024) and others.
        Large  libraries of ordinary and Brauer character tables and Tables of
        Marks are included as packages.
  
  4   The  documentation.  This  is  available as on-line help, as printable
        files in PDF format and as HTML for viewing with a Web browser.
  
  Also  included  with  the  core  system  are some test files and a few small
  utilities which we hope you will find useful.
  
  GAP  packages  are  self-contained  extensions to the core system. A package
  contains  GAP code and its own documentation and may also contain data files
  or  external  programs  to  which  the GAP code provides an interface. These
  packages   may   be  loaded  into  GAP  using  the  LoadPackage  (Reference:
  LoadPackage)  command,  and  both the package and its documentation are then
  available  just  as if they were parts of the core system. Some packages may
  be  loaded  automatically,  when  GAP  is started, if they are present. Some
  packages, because they depend on external programs, may only be available on
  the operating systems where those programs are available (usually UNIX). You
  should note that, while the packages included with this release are the most
  recent  versions  ready  for  release  at  this  time,  new packages and new
  versions  may  be  released  at any time and can be easily installed in your
  copy of GAP.
  
  With  GAP  there  are  two  packages  (the  library  of  ordinary and Brauer
  character  tables,  and  the  library  of  tables  of  marks)  which contain
  functionality  developed  from parts of the GAP core system. These have been
  moved  into packages for ease of maintenance and to allow new versions to be
  released  independently  of  new releases of the core system. The library of
  small  groups  should  also  be  regarded as a package, although it does not
  currently  use  the  standard  package  mechanism.  Other  packages  contain
  functionality  which  has never been part of the core system, and may extend
  it   substantially,   implementing   specific   algorithms  to  enhance  its
  capabilities, providing data libraries, interfaces to other computer algebra
  systems  and  data  sources  such  as the electronic version of the Atlas of
  Finite  Group Representations; therefore, installation and usage of packages
  is recommended.
  
  Further details about GAP packages can be found in chapter 'Reference: Using
  GAP      Packages',      and      on      the      GAP     website     here:
  https://www.gap-system.org/Packages/packages.html.
  
  
  1.2 Further Information about GAP
  
  Information about GAP is best obtained from the GAP website
  
  https://www.gap-system.org
  
  There you will find, amongst other things
  
      directions  to  the  sites from which you can download the current GAP
        distribution, all accepted and deposited GAP packages, and a selection
        of other contributions.
  
      the GAP manual and an archive of the gap-forum mailing list, formatted
        for reading with a Web browser, and indexed for searching.
  
      information  about  GAP  developers,  and  about  the  email addresses
        available for comment, discussion and support.
  
  We would particularly ask you to note the following things:
  
      The GAP Forum – an email discussion forum for comments, discussions or
        questions  about  GAP.  You  must subscribe to the list before you can
        post  to  it,  see  the  website  for  details.  In particular we will
        announce new releases in this mailing list.
  
      The email address mailto:[email protected] to which you are asked
        to send any questions or bug reports which do not seem likely to be of
        interest  to  the  whole GAP Forum. Please give a (short, if possible)
        self-contained  excerpt  of  a  GAP  session containing both input and
        output  that  illustrates  your problem (including comments of why you
        think  it  is  a  bug)  and  state  the type of the machine, operating
        system,  (compiler used, if UNIX/Linux) and the version of GAP you are
        using  (the  first  line  after the GAP 4 banner starting GAP, Version
        4...).
  
      We     also    ask    you    to    send    a    brief    message    to
        mailto:[email protected] when you install GAP.
  
      The correct form of citation of GAP, which we ask you use whenever you
        publish scientific results obtained using GAP.
  
  It finally remains for us to wish you all pleasure and success in using GAP,
  and to invite your constructive comment and criticism.
  
  The GAP Group,
  
  15-Jan-2018