  
  [1X1 [33X[0;0YPreface[133X[101X
  
  [33X[0;0YWelcome  to  [5XGAP[105X.  This is one of three manuals documenting the core part of
  [5XGAP[105X,  the  other  being  the  [13X[5XGAP[105X  Tutorial[113X  . and the document called [13X[21X[5XGAP[105X -
  Changes from Earlier Versions[121X[113X .[133X
  
  [33X[0;0YThis preface serves not only to introduce [21XThe [5XGAP[105X Reference Manual[121X, but also
  as an introduction to the whole system.[133X
  
  [33X[0;0Y[5XGAP[105X  stands  for  [13XGroups, Algorithms and Programming[113X. The name was chosen to
  reflect the aim of the system, which is introduced in this reference 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.[133X
  
  [33X[0;0YThis  manual,  the [13X[5XGAP[105X reference manual[113X contains the official definitions of
  [5XGAP[105X  functions. It should contain all the information needed to use [5XGAP[105X, and
  is not intended to be read cover-to-cover.[133X
  
  [33X[0;0YTo get started a new user may first look at parts of the [13X[5XGAP[105X Tutorial[113X .[133X
  
  [33X[0;0YA  lot  of  the  functionality  of  the  system  and a number of contributed
  extensions are provided as [21X[5XGAP[105X packages[121X which are developed independently of
  the  core  part  of  [5XGAP[105X  and can be loaded into a [5XGAP[105X session. Each package
  comes  with  a  its  own manual which is also available through the [5XGAP[105X help
  system.[133X
  
  [33X[0;0YThis  manual  is  divided into chapters, sections and subsections. Chapter [14X2[114X
  describes  the  [13Xhelp system[113X, which provides access to all the manuals from a
  running  [5XGAP[105X  session.  Chapter [14X3[114X  gives  technical  advice for [13Xrunning[113X [5XGAP[105X.
  Chapter [14X4[114X  introduces  the [5XGAP[105X language, and the next chapters deal with the
  [13Xenvironment[113X  provided  by  [5XGAP[105X  for the user. These are followed by the main
  bulk  of  chapters  which are devoted to the various mathematical structures
  that [5XGAP[105X can handle.[133X
  
  [33X[0;0YSubsequent  sections of this preface explain the structure of the system and
  provide copyright and licensing information.[133X
  
  
  [1X1.1 [33X[0;0YThe [5XGAP[105X[101X[1X System[133X[101X
  
  [33X[0;0Y[5XGAP[105X  is  a  [13Xfree[113X,  [13Xopen[113X  and  [13Xextensible[113X software package for computation in
  discrete  abstract  algebra. The terms [21Xfree[121X and [21Xopen[121X describe the conditions
  under  which  the  system  is  distributed -- in brief, it is [13Xfree of charge[113X
  (except  possibly  for the immediate costs of delivering it to you), you are
  [13Xfree  to  pass  it  on[113X within certain limits, and all of the workings of the
  system  are  [13Xopen for you to examine and change[113X. Details of these conditions
  can be found in Section [14X'Reference: Copyright and License'[114X.[133X
  
  [33X[0;0YThe  system is [21Xextensible[121X in that you can write your own programs in the [5XGAP[105X
  language,  and use them in just the same way as the programs which form part
  of  the  system (the [21Xlibrary[121X). Indeed, we actively support the contribution,
  refereeing  and distribution of extensions to the system, in the form of [21X[5XGAP[105X
  packages[121X.  Further details of this can be found in chapter [14X'Reference: Using
  and Developing GAP Packages'[114X, and on our website.[133X
  
  [33X[0;0YDevelopment  of  [5XGAP[105X 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 [5XGAP[105X 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 [5XGAP[105X 4.4 release
  in  2004,  which  has  been coordinated from Colorado State University, Fort
  Collins.[133X
  
  [33X[0;0YMore  information  on  the motivation and development of [5XGAP[105X to date, can be
  found on our Web pages in a section entitled [21XRelease history and Prefaces[121X                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          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