  
  [1X7 [33X[0;0YChanges from Earlier Versions[133X[101X
  
  
  [1X7.1 [33X[0;0YChanges between [5XGAP[105X[101X[1X 4.3 and [5XGAP[105X[101X[1X 4.4[133X[101X
  
  [33X[0;0YThe main changes between [5XGAP[105X 4.3 and [5XGAP[105X 4.4 are:[133X
  
  
  [1X7.1-1 [33X[0;0YPotentially Incompatible Changes[133X[101X
  
  [30X    [33X[0;6YThe  mechanism for the loading of Packages has changed to allow easier
        updates  independent  of  main  [5XGAP[105X  releases. Packages require a file
        [11XPackageInfo.g[111X  now.  The new [11XPackageInfo.g[111X files are available for all
        packages with the new version of GAP (see [14XExample: PackageInfo.g for a
        GAP package[114X).[133X
  
  [30X    [33X[0;6Y[2XIsSimpleGroup[102X  ([14XReference:  IsSimpleGroup[114X)  returns  false now for the
        trivial group.[133X
  
  [30X    [33X[0;6Y[2XPrimeBlocks[102X ([14XReference: PrimeBlocks[114X): The output format has changed.[133X
  
  [30X    [33X[0;6YDivision  rings  (see  [2XIsDivisionRing[102X ([14XReference: IsDivisionRing[114X)) are
        now implemented as [2XIsRingWithOne[102X ([14XReference: IsRingWithOne[114X).[133X
  
  [30X    [33X[0;6Y[2XDirectSumOfAlgebras[102X ([14XReference: DirectSumOfAlgebras for two algebras[114X):
        [22Xp[122X-th power maps are compatible with the input now.[133X
  
  [30X    [33X[0;6YThe print order for polynomials has been changed.[133X
  
  [33X[0;0YThese  changes  are,  in  some  respects,  departures  from  our  policy  of
  maintaining  upward  compatibility of documented functions between releases.
  In  the  first  case,  we  felt  that  the  old  behavior  was  sufficiently
  inconsistent,   illogical,  and  impossible  to  document  that  we  had  no
  alternative  but  to  change  it.  In the case of the package interface, the
  change  was necessary to introduce new functionality. The planned and phased
  removal  of  a  few  unnecessary  functions  or  synonyms is needed to avoid
  becoming  buried in [21Xlegacy[121X interfaces, but we remain committed to our policy
  of maintaining upward compatibility whenever sensibly possible.[133X
  
  [30X    [33X[0;6YGroebner Bases:[133X
  
        [33X[0;6YBuchberger's  algorithm to compute Groebner Bases has been implemented
        in GAP. (A. Hulpke)[133X
  
  [30X    [33X[0;6YFor large scale Groebner Basis computations there also is an interface
        to     the    Singular    system    available    in    the    [5XSingular[105X
        ([7Xhttps://www.gap-system.org/Packages/singular.html[107X)    package.    (M.
        Costantini and W. de Graaf)[133X
  
  [30X    [33X[0;6YNew  methods  for factorizing polynomials over algebraic extensions of
        the rationals have been implemented in GAP. (A. Hulpke)[133X
  
  [30X    [33X[0;6YFor  more  functionality to compute with algebraic number fields there
        is   an   interface  to  the  Kant  system  available  in  the  [5XAlnuth[105X
        ([7Xhttps://www.gap-system.org/Packages/alnuth.html[107X) package. (B. Assmann
        and B. Eick)[133X
  
  [30X    [33X[0;6YA  new  functionality  to  compute  the  minimal normal subgroups of a
        finite group, as well as its socle, has been installed. (B. Höfling)[133X
  
  [30X    [33X[0;6YA fast method for recognizing whether a permutation group is symmetric
        or alternating is available now (A. Seress)[133X
  
  [30X    [33X[0;6YA  method  for  computing the Galois group of a rational polynomial is
        available again. (A. Hulpke)[133X
  
  [30X    [33X[0;6YThe      algorithm      for      [2XBrauerCharacterValue[102X      ([14XReference:
        BrauerCharacterValue[114X)   has  been  extended  to  the  case  where  the
        splitting field is not supported in [5XGAP[105X. (T. Breuer)[133X
  
  [30X    [33X[0;6YBrauer tables of direct products can now be constructed from the known
        Brauer tables of the direct factors. (T. Breuer)[133X
  
  [30X    [33X[0;6YBasic  support  for  vector  spaces  of  rational functions and of uea
        elements is available now in [5XGAP[105X. (T. Breuer and W. de Graaf)[133X
  
  [30X    [33X[0;6YVarious  new  functions  for  computations  with  integer matrices are
        available,  such  as  methods  for  computing  normal forms of integer
        matrices  as well as nullspaces or solutions systems of equations. (W.
        Nickel and F. Gähler)[133X
  
  
  [1X7.1-2 [33X[0;0YNew Packages[133X[101X
  
  [33X[0;0YThe following new Packages have been accepted.[133X
  
  [30X    [33X[0;6Y[5XAlnuth[105X:  Algebraic  Number Theory and an interface to the Kant system.
        ([7Xhttps://www.gap-system.org/Packages/alnuth.html[107X) By B. Assmann and B.
        Eick.[133X
  
  [30X    [33X[0;6Y[5XLAGUNA[105X:  Computing  with  Lie  Algebras  and  Units of Group Algebras.
        ([7Xhttps://www.gap-system.org/Packages/laguna.html[107X)   By  V.  Bovdi,  A.
        Konovalov, R. Rossmanith, C. Schneider.[133X
  
  [30X    [33X[0;6Y[5XNQ[105X:       The       ANU       Nilpotent       Quotient      Algorithm.
        ([7Xhttps://www.gap-system.org/Packages/nq.html[107X) By W. Nickel.[133X
  
  [30X    [33X[0;6Y[5XKBMAG[105X:       Knuth-Bendix       for      Monoids      and      Groups.
        ([7Xhttps://www.gap-system.org/Packages/kbmag.html[107X) By D. Holt.[133X
  
  [30X    [33X[0;6Y[5XPolycyclic[105X:       Computation       with       polycyclic      groups.
        ([7Xhttps://www.gap-system.org/Packages/polycyclic.html[107X)  By  B. Eick and
        W. Nickel.[133X
  
  [30X    [33X[0;6Y[5XQuaGroup[105X:    Computing    with    Quantized    Enveloping    Algebras.
        ([7Xhttps://www.gap-system.org/Packages/quagroup.html[107X) By W. de Graaf.[133X
  
  
  [1X7.1-3 [33X[0;0YPerformance Enhancements[133X[101X
  
  [30X    [33X[0;6YThe   computation   of  irreducible  representations  and  irreducible
        characters  using the Baum-Clausen algorithm and the implementation of
        the Dixon-Schneider algorithm have been speeded up.[133X
  
  [30X    [33X[0;6YThe      algorithm      for      [2XPossibleClassFusions[102X      ([14XReference:
        PossibleClassFusions[114X) has been changed: the efficiency is improved and
        a new criterion is used. The algorithm for [2XPossibleFusionsCharTableTom[102X
        ([14XReference:  PossibleFusionsCharTableTom[114X)  has  been  speeded  up. The
        method  for  [2XPrimeBlocks[102X  ([14XReference:  PrimeBlocks[114X)  has been improved
        following a suggestion of H. Pahlings.[133X
  
  [30X    [33X[0;6YNew  improved  methods  for normalizer and subgroup conjugation in [22XS_n[122X
        have     been    installed    and    new    improved    methods    for
        [2XIsNaturalSymmetricGroup[102X   ([14XReference:   IsNaturalSymmetricGroup[114X)   and
        [2XIsNaturalAlternatingGroup[102X  ([14XReference: IsNaturalAlternatingGroup[114X) have
        been  implemented.  These improve the available methods when groups of
        large degrees are given.[133X
  
  [30X    [33X[0;6YThe partition split method used in the permutation backtrack is now in
        the  kernel.  Transversal computations in large permutation groups are
        improved.  Homomorphisms  from free groups into permutation groups now
        give substantially shorter words for preimages.[133X
  
  [30X    [33X[0;6YThe membership test in [2XSP[102X ([14XReference: Sp for dimension and field size[114X)
        and  [2XSU[102X  ([14XReference:  SU[114X) groups has been improved using the invariant
        forms underlying these groups.[133X
  
  [30X    [33X[0;6YAn  improvement for the cyclic extension method for the computation of
        subgroup lattices has been implemented.[133X
  
  [30X    [33X[0;6YA  better  method for [2XMinimalPolynomial[102X ([14XReference: MinimalPolynomial[114X)
        for finite field matrices has been implemented.[133X
  
  [30X    [33X[0;6YThe display has changed and the arithmetic of multivariate polynomials
        has been improved.[133X
  
  [30X    [33X[0;6YThe  [2XLogMod[102X ([14XReference: LogMod[114X) function now uses Pollard's rho method
        combined with the Pohlig/Hellmann approach.[133X
  
  [30X    [33X[0;6YVarious  functions  for  sets  and  lists have been improved following
        suggestions  of  L.  Teirlinck. These include: [2XSort[102X ([14XReference: Sort[114X),
        [2XSortex[102X  ([14XReference:  Sortex[114X),  [2XSortParallel[102X ([14XReference: SortParallel[114X),
        [2XSortingPerm[102X   ([14XReference:   SortingPerm[114X),  [2XNrArrangements[102X  ([14XReference:
        NrArrangements[114X).[133X
  
  [30X    [33X[0;6YThe      methods      for      [2XStructureConstantsTable[102X     ([14XReference:
        StructureConstantsTable[114X)      and      [2XGapInputSCTable[102X     ([14XReference:
        GapInputSCTable[114X)  have  been  improved  in the case of a known (anti-)
        symmetry following a suggestion of M. Costantini.[133X
  
  [33X[0;0YThe  improvements  listed in this Section have been implemented by T. Breuer
  and A. Hulpke.[133X
  
  
  [1X7.1-4 [33X[0;0YNew Programming and User Features[133X[101X
  
  [30X    [33X[0;6YThe  2GB limit for workspace size has been removed and version numbers
        for saved workspaces have been introduced. (S. Linton and B. Höfling)[133X
  
  [30X    [33X[0;6YThe  limit  on the total number of types created in a session has been
        removed. (S. Linton)[133X
  
  [30X    [33X[0;6YThere is a new mechanism for loading packages available. Packages need
        a  file  [11XPackageInfo.g[111X  now.  (T.  Breuer  and F. Lübeck; see [14XExample:
        PackageInfo.g for a GAP package[114X).[133X
  
  [33X[0;0YFinally,  as  always,  a  number  of bugs have been fixed. This release thus
  incorporates  the  contents of all the bug fixes which were released for [5XGAP[105X
  4.3. It also fixes a number of bugs discovered since the last bug fix.[133X
  
  
  [1X7.2 [33X[0;0YEarlier Changes[133X[101X
  
  [33X[0;0YThe most important changes between [5XGAP[105X 4.2 and [5XGAP[105X 4.3 were:[133X
  
  [30X    [33X[0;6YThe performance of several routines has been substantially improved.[133X
  
  [30X    [33X[0;6YThe  functionality  in  the  areas of finitely presented groups, Schur
        covers and the calculation of representations has been extended.[133X
  
  [30X    [33X[0;6YThe  data  libraries  of  transitive  groups,  finite  integral matrix
        groups, character tables and tables of marks have been extended.[133X
  
  [30X    [33X[0;6YThe  Windows  installation  has been simplified for the case where you
        are installing [5XGAP[105X in its standard location.[133X
  
  [30X    [33X[0;6YMany bugs have been fixed.[133X
  
  [33X[0;0YThe most important changes between [5XGAP[105X 4.1 and [5XGAP[105X 4.2 were:[133X
  
  [30X    [33X[0;6YA  much  extended  and  improved  library  of  small groups as well as
        associated [2XIdGroup[102X ([14XReference: IdGroup[114X) routines.[133X
  
  [30X    [33X[0;6YThe  primitive  groups  library  has been made more independent of the
        rest of [5XGAP[105X, some errors were corrected.[133X
  
  [30X    [33X[0;6YNew  (and  often  much  faster)  infrastructure for orbit computation,
        based on a general [21Xdictionary[121X abstraction.[133X
  
  [30X    [33X[0;6YNew functionality for dealing with representations of algebras, and in
        particular for semisimple Lie algebras.[133X
  
  [30X    [33X[0;6YNew  functionality  for binary relations on arbitrary sets, magmas and
        semigroups.[133X
  
  [30X    [33X[0;6YBidirectional  streams, allowing an external process to be started and
        then controlled [21Xinteractively[121X by [5XGAP[105X[133X
  
  [30X    [33X[0;6YA  prototype  implementation  of  algorithms  using  general  subgroup
        chains.[133X
  
  [30X    [33X[0;6YChanges in the behavior of vectors over small finite fields.[133X
  
  [30X    [33X[0;6YA  fifth  book  [21XNew  features for Developers[121X has been added to the [5XGAP[105X
        manual.[133X
  
  [30X    [33X[0;6YNumerous bug fixes and performance improvements[133X
  
  [33X[0;0YThe changes between the final release of [5XGAP[105X 3 (version 3.4.4) and [5XGAP[105X 4 are
  wide-ranging.  The  general  philosophy of the changes is two-fold. Firstly,
  many  assumptions  in  the  design  of  [5XGAP[105X  3 revealed its authors' primary
  interest  in  group theory, and indeed in finite group theory. Although much
  of  the  [5XGAP[105X 4 library is concerned with groups, the basic design now allows
  extension  to  other  algebraic structures, as witnessed by the inclusion of
  substantial  bodies  of  algorithms  for computation with semigroups and Lie
  algebras.  Secondly,  as  the  scale of the system, and the number of people
  using  and  contributing  to  it  has  grown, some aspects of the underlying
  system  have  proved to be restricting, and these have been improved as part
  of  comprehensive  re-engineering  of  the system. This has included the new
  method  selection  system, which underpins the library, and a new, much more
  flexible, [5XGAP[105X package interface.[133X
  
  [33X[0;0YDetails  of  these  changes  can be found in the document [21XMigrating to GAP 4[121X
  available          at          the          [5XGAP[105X         website,         see
  [7Xhttps://www.gap-system.org/Gap3/migratedoc.pdf[107X.[133X
  
  [33X[0;0YIt is perhaps worth mentioning a few points here.[133X
  
  [33X[0;0YFirstly,  much  remains  unchanged, from the perspective of the mathematical
  user:[133X
  
  [30X    [33X[0;6YThe  syntax  of that part of the [5XGAP[105X language that most users need for
        investigating mathematical problems.[133X
  
  [30X    [33X[0;6YThe great majority of function names.[133X
  
  [30X    [33X[0;6YData libraries and the access to them.[133X
  
  [33X[0;0YA number of visible aspects have changed:[133X
  
  [30X    [33X[0;6YSome  function names that need finer specifications now that there are
        more structures available in [5XGAP[105X.[133X
  
  [30X    [33X[0;6YThe  access  to  information  already  obtained  about  a mathematical
        structure.  In [5XGAP[105X 3 such information about a group could be looked up
        by  directly  inspecting  the group record, whereas in [5XGAP[105X 4 functions
        must be used to access such information.[133X
  
  [33X[0;0YBehind the scenes, much has changed:[133X
  
  [30X    [33X[0;6YA  new  kernel,  with  improvements  in  memory  management and in the
        language  interpreter,  as  well  as  new  features  such as saving of
        workspaces and the possibility of compilation of [5XGAP[105X code into C.[133X
  
  [30X    [33X[0;6YA  new  structure  to  the  library,  based upon a new type and method
        selection  system,  which  is  able  to  support  a  broader  range of
        algebraic computation and to make the structure of the library simpler
        and more modular.[133X
  
  [30X    [33X[0;6YNew and faster algorithms in many mathematical areas.[133X
  
  [30X    [33X[0;6YData  structures  and algorithms for new mathematical objects, such as
        algebras and semigroups.[133X
  
  [30X    [33X[0;6YA  new  and  more  flexible  structure  for  the  [5XGAP[105X installation and
        documentation,  which  means,  for example, that a [5XGAP[105X package and its
        documentation can be installed and be fully usable without any changes
        to the [5XGAP[105X system.[133X
  
  [33X[0;0YVery few features of [5XGAP[105X 3 are not yet available in [5XGAP[105X 4.[133X
  
  [30X    [33X[0;6YNot  all  of  the  [5XGAP[105X 3 packages have yet been converted for use with
        [5XGAP[105X 4.[133X
  
  [30X    [33X[0;6YThe  library  of crystallographic groups which was present in [5XGAP[105X 3 is
        now       part       of       a       [5XGAP[105X 4      package      [5XCrystCat[105X
        ([7Xhttps://www.gap-system.org/Packages/crystcat.html[107X)  by  V. Felsch and
        F. Gähler.[133X
  
