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  8 Changes between GAP 4.3 and GAP 4.4
  
  This  chapter  contains  an overview of most important changes introduced in
  GAP  4.4.  It  also contains information about subsequent update releases of
  GAP 4.4.
  
  
  8.1 Changes in the core GAP system introduced in GAP 4.4
  
  
  8.1-1 Potentially Incompatible Changes
  
      The  mechanism for the loading of Packages has changed to allow easier
        updates  independent  of  main  GAP  releases. Packages require a file
        PackageInfo.g  now.  The new PackageInfo.g files are available for all
        packages with the new version of GAP (see Reference: PackageInfo.g for
        a GAP package).
  
      IsSimpleGroup  (Reference:  IsSimpleGroup)  returns  false now for the
        trivial group.
  
      PrimeBlocks (Reference: PrimeBlocks): The output format has changed.
  
      Division  rings  (see  IsDivisionRing (Reference: IsDivisionRing)) are
        now implemented as IsRingWithOne (Reference: IsRingWithOne).
  
      DirectSumOfAlgebras (Reference: DirectSumOfAlgebras for two algebras):
        p-th power maps are compatible with the input now.
  
      The print order for polynomials has been changed.
  
  These  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 legacy interfaces, but we remain committed to our policy
  of maintaining upward compatibility whenever sensibly possible.
  
      Groebner Bases:
  
        Buchberger's  algorithm to compute Groebner Bases has been implemented
        in GAP. (A. Hulpke)
  
      For large scale Groebner Basis computations there also is an interface
        to     the    Singular    system    available    in    the    Singular
        (https://www.gap-system.org/Packages/singular.html)    package.    (M.
        Costantini and W. de Graaf)
  
      New  methods  for factorizing polynomials over algebraic extensions of
        the rationals have been implemented in GAP. (A. Hulpke)
  
      For  more  functionality to compute with algebraic number fields there
        is   an   interface  to  the  Kant  system  available  in  the  Alnuth
        (https://www.gap-system.org/Packages/alnuth.html) package. (B. Assmann
        and B. Eick)
  
      A  new  functionality  to  compute  the  minimal normal subgroups of a
        finite group, as well as its socle, has been installed. (B. Höfling)
  
      A fast method for recognizing whether a permutation group is symmetric
        or alternating is available now (A. Seress)
  
      A  method  for  computing the Galois group of a rational polynomial is
        available again. (A. Hulpke)
  
      The      algorithm      for      BrauerCharacterValue      (Reference:
        BrauerCharacterValue)   has  been  extended  to  the  case  where  the
        splitting field is not supported in GAP. (T. Breuer)
  
      Brauer tables of direct products can now be constructed from the known
        Brauer tables of the direct factors. (T. Breuer)
  
      Basic  support  for  vector  spaces  of  rational functions and of uea
        elements is available now in GAP. (T. Breuer and W. de Graaf)
  
      Various  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)
  
  
  8.1-2 New Packages
  
  The following new Packages have been accepted.
  
      Alnuth:  Algebraic  Number Theory and an interface to the Kant system.
        (https://www.gap-system.org/Packages/alnuth.html) By B. Assmann and B.
        Eick.
  
      LAGUNA:  Computing  with  Lie  Algebras  and  Units of Group Algebras.
        (https://www.gap-system.org/Packages/laguna.html)   By  V.  Bovdi,  A.
        Konovalov, R. Rossmanith, C. Schneider.
  
      NQ:       The       ANU       Nilpotent       Quotient      Algorithm.
        (https://www.gap-system.org/Packages/nq.html) By W. Nickel.
  
      KBMAG:       Knuth-Bendix       for      Monoids      and      Groups.
        (https://www.gap-system.org/Packages/kbmag.html) By D. Holt.
  
      Polycyclic:       Computation       with       polycyclic      groups.
        (https://www.gap-system.org/Packages/polycyclic.html)  By  B. Eick and
        W. Nickel.
  
      QuaGroup:    Computing    with    Quantized    Enveloping    Algebras.
        (https://www.gap-system.org/Packages/quagroup.html) By W. de Graaf.
  
  
  8.1-3 Performance Enhancements
  
      The   computation   of  irreducible  representations  and  irreducible
        characters  using the Baum-Clausen algorithm and the implementation of
        the Dixon-Schneider algorithm have been speeded up.
  
      The      algorithm      for      PossibleClassFusions      (Reference:
        PossibleClassFusions) has been changed: the efficiency is improved and
        a new criterion is used. The algorithm for PossibleFusionsCharTableTom
        (Reference:  PossibleFusionsCharTableTom)  has  been  speeded  up. The
        method  for  PrimeBlocks  (Reference:  PrimeBlocks)  has been improved
        following a suggestion of H. Pahlings.
  
      New  improved  methods  for normalizer and subgroup conjugation in S_n
        have     been    installed    and    new    improved    methods    for
        IsNaturalSymmetricGroup   (Reference:   IsNaturalSymmetricGroup)   and
        IsNaturalAlternatingGroup  (Reference: IsNaturalAlternatingGroup) have
        been  implemented.  These improve the available methods when groups of
        large degrees are given.
  
      The 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.
  
      The membership test in SP (Reference: Sp for dimension and field size)
        and  SU  (Reference:  SU) groups has been improved using the invariant
        forms underlying these groups.
  
      An  improvement for the cyclic extension method for the computation of
        subgroup lattices has been implemented.
  
      A  better  method for MinimalPolynomial (Reference: MinimalPolynomial)
        for finite field matrices has been implemented.
  
      The display has changed and the arithmetic of multivariate polynomials
        has been improved.
  
      The  LogMod (Reference: LogMod) function now uses Pollard's rho method
        combined with the Pohlig/Hellmann approach.
  
      Various  functions  for  sets  and  lists have been improved following
        suggestions  of  L.  Teirlinck. These include: Sort (Reference: Sort),
        Sortex  (Reference:  Sortex),  SortParallel (Reference: SortParallel),
        SortingPerm   (Reference:   SortingPerm),  NrArrangements  (Reference:
        NrArrangements).
  
      The      methods      for      StructureConstantsTable     (Reference:
        StructureConstantsTable)      and      GapInputSCTable     (Reference:
        GapInputSCTable)  have  been  improved  in the case of a known (anti-)
        symmetry following a suggestion of M. Costantini.
  
  The  improvements  listed in this Section have been implemented by T. Breuer
  and A. Hulpke.
  
  
  8.1-4 New Programming and User Features
  
      The  2GB limit for workspace size has been removed and version numbers
        for saved workspaces have been introduced. (S. Linton and B. Höfling)
  
      The  limit  on the total number of types created in a session has been
        removed. (S. Linton)
  
      There is a new mechanism for loading packages available. Packages need
        a  file  PackageInfo.g  now.  (T. Breuer and F. Lübeck; see Reference:
        PackageInfo.g for a GAP package).
  
  Finally,  as  always,  a  number  of bugs have been fixed. This release thus
  incorporates  the  contents of all the bug fixes which were released for GAP
  4.3. It also fixes a number of bugs discovered since the last bug fix.
  
  Below we list changes in the main system (excluding packages) that have been
  corrected or added in bugfixes and updates for GAP 4.4.
  
  
  8.2 GAP 4.4 Bugfix 2 (April 2004)
  
  Fixed bugs which could lead to crashes:
  
      A crash when incorrect types of arguments are passed to FileString.
  
  Other fixed bugs:
  
      A bug in DerivedSubgroupTom and DerivedSubgroupsTom.
  
      An error in the inversion of certain ZmodnZObj elements.
  
      A wrong display string of the numerator in rational functions returned
        by  MolienSeriesWithGivenDenominator  (in  the  case that the constant
        term of this numerator is zero).
  
  
  8.3 GAP 4.4 Bugfix 3 (May 2004)
  
  Fixed bugs which could produce wrong results:
  
      Incorrect  setting  of  system  variables  (e.g.,  home  directory and
        command line options) after loading a workspace.
  
      Wrong handling of integer literals within functions or loops on 64-bit
        architectures (only integers in the range from 2^28 to 2^60).
  
  Fixed bugs which could lead to crashes:
  
      A  problem  in  the  installation  of  the  multiplication routine for
        matrices   that  claimed  to  be  applicable  for  more  general  list
        multiplications.
  
      A  problem when computing weight distributions of codes with weights >
        2^28.
  
  Other fixed bugs:
  
      Problems with the online help with some manual sections.
  
      Problems of the online help on Windows systems.
  
      A  problem  in GQuotients when mapping from a finitely presented group
        which has a free direct factor.
  
      A bug in the function DisplayRevision.
  
      The  trivial  finitely  presented  group  on  no  generators  was  not
        recognized as finitely presented.
  
      A problem with Process.
  
      A  problem  when  intersecting  subgroups of finitely presented groups
        that  are represented in quotient representation with the quotient not
        apermutation group.
  
      A  bug  in  the generic Intersection2 method for vector spaces, in the
        case that both spaces are trivial.
  
      Enable ReeGroup(q) for q = 3.
  
  
  8.4 GAP 4.4 Bugfix 4 (December 2004)
  
  Fixed bugs which could produce wrong results:
  
      An error in the Order method for matrices over cyclotomic fields which
        caused  this method to return infinity for matrices of finite order in
        certain cases.
  
      Representations     computed    by    IrreducibleRepresentations    in
        characteristic 0 erraneously claimed to be faithful.
  
      A  primitive  representation  of  degree  574  for  PSL(2,41) has been
        missing in the classification on which the GAP library was built.
  
      A  bug  in  Append for compressed vectors over GF(2): if the length of
        the result is 1 mod 32 (or 64) the last entry was forgotten to copy.
  
      A  problem  with  the  Ree  group  Ree(3)  of size 1512 claiming to be
        simple.
  
      An  error  in  the  membership test for groups GU(n,q) and SU(n,q) for
        non-prime q.
  
      An  error in the kernel code for ranges which caused e.g. -1 in [1..2]
        to return true.
  
      An error recording boolean lists in saved workspaces.
  
      A  problem  in  the  selection  function  for primitive and transitive
        groups if no degree is given.
  
      ReducedConfluentRewritingSystem  returning  a cached result that might
        not conform to the ordering specified.
  
  Other fixed bugs:
  
      A  problem  with  the  function  SuggestUpdates  to check for the most
        recent version of packages available.
  
      A  problem  that  caused  MatrixOfAction  to produce an error when the
        algebra module was constructed as a direct sum.
  
      Problems  with  computing n-th power maps of character tables, where n
        is  negative  and  the  table  does  not  yet  store  its  irreducible
        characters.
  
      Element  conjugacy  in  large-base  permutation  groups  sometimes was
        unnecessarily inefficient.
  
      A missing method for getting the letter representation of an associate
        word in straight line program representation.
  
      A  problem with the construction of vector space bases where the given
        list of basis vectors is itself an object that was returned by Basis.
  
      A  problem  of  AbelianInvariantsMultiplier insisting that a result of
        IsomorphismFpGroup is known to be surjective.
  
      An  error  in  the routine for Resultant if one of the polynomials has
        degree zero.
  
  
  8.5 GAP 4.4 Update 5 (May 2005)
  
  Fixed bugs which could produce wrong results:
  
      GroupWithGenerators   (Reference:   GroupWithGenerators)   returned  a
        meaningless  group  object  instead  of signaling an error when it was
        called with an empty list of generators.
  
      When  computing  preimages under an embedding into a direct product of
        permutation  groups,  if  the  element  was  not  in  the image of the
        embedding then a permutation had been returned instead of fail.
  
      Two  problems  with  PowerMod  (Reference:  PowerMod) for polynomials.
        [Reported by Jack Schmidt]
  
      Some  methods  for  computing  the  sum  of  ideals returned the first
        summand instead of the sum. [Reported by Alexander Konovalov]
  
      Wrong result in Intersection (Reference: Intersection) for pc groups.
  
      The  function CompareVersionNumbers (Reference: CompareVersionNumbers)
        erroneously ignored leading non-digit characters.
  
        A  new  feature in the corrected version is an optional third argument
        "equal",  which  causes  the function to return true only if the first
        two   arguments  describe  equal  version  numbers;  documentation  is
        available  in  the ext-manual. This new feature is used in LoadPackage
        (Reference:  LoadPackage), now one can require a specific version of a
        package.
  
        The  library  code still contained parts of the handling of completion
        files for packages, which does not work and therefore had already been
        removed from the documentation. This code has now been removed.
  
        Now a new component PreloadFile is supported in The PackageInfo.g File
        (Reference:  The  PackageInfo.g  File)  files; if it is bound then the
        file  in  question  is  read  immediately  before  the  package or its
        documentation is loaded.
  
      The   result   of  String  (Reference:  String)  for  strings  not  in
        IsStringRep  (Reference:  IsStringRep)  that  occur as list entries or
        record components was erroneously missing the double quotes around the
        strings.
  
      A  bug  which  caused InducedPcgs (Reference: InducedPcgs) to return a
        pcgs which is not induced wrt. the parent pcgs of pcgs. This may cause
        unpredictable   behaviour,   e. g.   when   SiftedPcElement   is  used
        subsequently. [Reported by Alexander Konovalov]
  
      Fixed a bug in SmallGroupsInformation(512).
  
      PowerModCoeffs   (Reference:   PowerModCoeffs)  with  exponent  1  for
        compressed  vectors did not reduce (a copy of) the input vector before
        returning it. [Reported by Frank Lübeck]
  
      Sorting  a  mutable  non-plain  list  (e.g.,  a compressed matrix over
        fields  of  order  <  257)  could  potentially  destroy  that  object.
        [Reported by Alexander Hulpke]
  
      Under  rare circumstances computing the closure of a permutation group
        by  a  normalizing element could produce a corrupted stabilizer chain.
        (The underlying algorithm uses random elements, probability of failure
        was below 1 percent). [Reported by Thomas Breuer]
  
  Fixed bugs which could lead to crashes:
  
      Some  code  and  comments  in  the GAP kernel assumed that there is no
        garbage  collection during the core printing function Pr, which is not
        correct.  This  could cause GAP in rare cases to crash during printing
        permutations,  cyclotomics  or  strings  with zero bytes. [Reported by
        Warwick Harvey]
  
  Other fixed bugs:
  
      A  rare  problem  with  the  choice  of  prime  in the Dixon-Schneider
        algorithm  for  computing the character table of a group. [Reported by
        Jack Schmidt]
  
      DirectProduct   (Reference:  DirectProduct)  for  trivial  permutation
        groups returned a strange object.
  
      A  problem  with  PolynomialReduction (Reference: PolynomialReduction)
        running into an infinite loop.
  
      Adding  linear mappings with different image domains was not possible.
        [Reported by Pasha Zusmanovich]
  
      Multiplying  group  ring  elements  with  rationals  was not possible.
        [Reported by Laurent Bartholdi]
  
      Random  (Reference: Random) now works for finite fields of size larger
        than 2^28. [Reported by Jack Schmidt]
  
      Univariate polynomial creators did modify the coefficient list passed.
        [Reported by Jürgen Müller]
  
      Fixed  IntHexString  (Reference: IntHexString) to accept arguments not
        in  IsStringRep;  the  argument  is  now first converted if necessary.
        [Reported by Kenn Heinrich]
  
      The  library  code for stabilizer chains contained quite some explicit
        references  to  the identity (). This is unfortunate if one works with
        permutation  groups,  the elements of which are not plain permutations
        but objects which carry additional information like a memory, how they
        were  obtained  from  the  group generators. For such cases it is much
        cleaner  to  use  the  One(...) operation instead of (), such that the
        library code can be used for a richer class of group objects. This fix
        contains  only  rather  trivial  changes  ()  to  One(...)  which were
        carefully  checked  by  me.  The  tests for permutation groups all run
        without a problem. However, it is relatively difficult to provide test
        code for this particular change, since the "improvement" only shows up
        when  one generates new group objects. This is for example done in the
        package  recog  which  is in preparation. [Reported by Akos Seress and
        Max Neunhöffer]
  
      Using  {}  to  select  elements  of  a  known  inhomogenous dense list
        produced  a  list  that  might falsely claim to be known inhomogenous,
        which  could  lead to a segfault if the list typing code tried to mark
        it homogenous, since the code intended to catch such errors also had a
        bug. [Reported by Steve Linton]
  
      The  record for the generic iterator construction of subspaces domains
        of non-row spaces was not complete.
  
      When  a  workspace has been created without packages(-A option) and is
        loaded into a GAP session without packages (same option) then an error
        message is printed.
  
      So   far   the   functions   IsPrimeInt  (Reference:  IsPrimeInt)  and
        IsProbablyPrimeInt (Reference: IsProbablyPrimeInt) are essentially the
        same   except  that  IsPrimeInt  issues  an  additional  warning  when
        (non-proven) probable primes are considered as primes.
  
        These warnings now print the probable primes in question as well; if a
        probable  prime is used several times then the warning is also printed
        several  times;  there  is  no  longer  a warning for some known large
        primes;  the  warnings can be switched off. See IsPrimeInt (Reference:
        IsPrimeInt) for more details.
  
        If  we  get  a  reasonable  primality  test  in GAP we will change the
        definition of IsPrimeInt to do a proper test.
  
      Corrected  some  names  of primitive groups in degree 26. [Reported by
        Robert F. Bailey]
  
  New or improved functionality:
  
      Several changes for ConwayPolynomial (Reference: ConwayPolynomial):
  
            many new pre-computed polynomials
  
            put data in several separate files (only read when needed)
  
            added info on origins of pre-computed polynomials
  
            improved    performance    of    ConwayPolynomial    (Reference:
              ConwayPolynomial)    and    IsPrimitivePolynomial    (Reference:
              IsPrimitivePolynomial) for p < 256
  
            improved documentation of ConwayPolynomial
  
            added   and  documented  new  functions  IsCheapConwayPolynomial
              (Reference:             IsCheapConwayPolynomial)             and
              RandomPrimitivePolynomial (Reference: RandomPrimitivePolynomial)
  
      Added  method for NormalBase (Reference: NormalBase) for extensions of
        finite fields.
  
      Added  more  help  viewers  for  the HTML version of the documentation
        (firefox, mozilla, konqueror, w3m, safari).
  
      New  function  ColorPrompt  (Reference: ColorPrompt). (Users of former
        versions   of   a   colorprompt.g   file:   Now   you   just   need  a
        ColorPrompt(true); in your .gaprc file.)
  
      Specialised  kernel functions to support GUAVA 2.0. GAP will only load
        GUAVA in version at least 2.002 after this update.
  
      Now  there  is  a  kernel  function  CYC_LIST for converting a list of
        rationals into a cyclotomic, without arithmetics overhead.
  
      New     functions     ContinuedFractionExpansionOfRoot     (Reference:
        ContinuedFractionExpansionOfRoot)                                  and
        ContinuedFractionApproximationOfRoot                       (Reference:
        ContinuedFractionApproximationOfRoot) for computing continued fraction
        expansions  and  continued  fraction  approximations  of real roots of
        polynomials with integer coefficients.
  
      A  method  for  computing  structure  descriptions  for finite groups,
        available via StructureDescription (Reference: StructureDescription).
  
      This  change  contains  the  new,  extended version of the SmallGroups
        package. For example, the groups of orders p^4, p^5, p^6 for arbitrary
        primes  p, the groups of square-free order and the groups of cube-free
        order  at  most  50000 are included now. For more detailed information
        see the announcement of the extended package.
  
      The  function  ShowPackageVariables  gives  an  overview of the global
        variables in a package. It is thought as a utility for package authors
        and referees. (It uses the new function IsDocumentedVariable.)
  
      The mechanisms for testing GAP has been improved:
  
            The  information  whether  a  test  file  belongs to the list in
              tst/testall.g is now stored in the test file itself.
  
            Some  targets for testing have been added to the Makefile in the
              GAP  root  directory,  the  output  of the tests goes to the new
              directory dev/log.
  
            Utility   functions   for   testing   are   in   the   new  file
              tst/testutil.g. Now the loops over (some or all) files tst/*.tst
              can   be   performed   with   a  function  call,  and  the  file
              tst/testall.g   can   be   created   automatically;   the   file
              tst/testfull.g  is  now  obsolete.  The  remormalization  of the
              scaling  factors  can  now  be done using a GAP function, so the
              file tst/renorm.g is obsolete.
  
            Now  the  functions  START_TEST  and STOP_TEST use components in
              GAPInfo  instead of own globals, and the random number generator
              is always reset in START_TEST.
  
            GAPInfo.SystemInformation  now  takes two arguments, now one can
              use it easier in the tests.
  
      MultiplicationTable   (Reference:   MultiplicationTable)   is  now  an
        attribute,  and  the  construction  of  a  magma,  monoid,  etc.  from
        multiplication tables has been unified.
  
  
  8.6 GAP 4.4 Update 6 (September 2005)
  
  Attribution  of  bugfixes and improved functionalities to those who reported
  or provided these, respectively, is still fairly incomplete and inconsistent
  with this update. We apologise for this fact and will discuss until the next
  update how to improve this feature.
  
  Fixed bugs which could produce wrong results:
  
      The  perfect  group  library  does  not contain any information on the
        trivial  group,  so  the  trivial  group  must  be  handled specially.
        PerfectGroup (Reference: PerfectGroup) and NrPerfectLibraryGroups were
        changed to indicate that the trivial group is not part of the library.
  
      The  descriptions of PerfectGroup(734832,3) and PerfectGroup(864000,3)
        were corrected in the Finite Perfect Groups (Reference: Finite Perfect
        Groups) library of perfect groups.
  
      The functions EpimorphismSchurCover (Reference: EpimorphismSchurCover)
        and               AbelianInvariantsMultiplier              (Reference:
        AbelianInvariantsMultiplier)  may  have produced wrong results without
        warning  [Reported  by  Colin  Ingalls].  These  problems  are  fixed.
        However,  the methods currently used can be expected to be slower than
        the ones used before; we hope to fix this in the next version of GAP.
  
      DerivedSubgroup  (Reference:  DerivedSubgroup)  and CommutatorSubgroup
        (Reference:   CommutatorSubgroup)  for  permutation  groups  sometimes
        returned  groups  with  an incorrect stabilizer chain due to a missing
        verification step after a random Schreier Sims.
  
      NaturalHomomorphismByNormalSubgroup                        (Reference:
        NaturalHomomorphismByNormalSubgroup)   for  FpGroups  did  unnecessary
        rewrites.
  
      The alternating group A_3 incorrectly claimed to be not simple.
  
      ExponentSyllable   (Reference:  ExponentSyllable)  for  straight  line
        program elements gave a wrong result.
  
      PrimePGroup  (Reference:  PrimePGroup)  is  defined to return fail for
        trivial  groups,  but  if  the  group  was  constructed as a factor or
        subgroup of a known p-group, the value of p was retained.
  
      The        functions        TestPackageAvailability        (Reference:
        TestPackageAvailability)  and LoadPackage (Reference: LoadPackage) did
        not  work  correctly  when  one  asked for a particular version of the
        package,  via  a  version number starting with the character =, in the
        sense that a version with a larger version number was loaded if it was
        available. [Reported by Burkhard Höfling]
  
      The   generator   names   constructed  by  AlgebraByStructureConstants
        (Reference: AlgebraByStructureConstants) were nonsense.
  
      The   undocumented  function  (but  recently  advertised  on  gap-dev)
        COPY_LIST_ENTRIES  did  not  handle overlapping source and destination
        areas correctly in some cases.
  
      The elements in a free magma ring have the filter IsAssociativeElement
        (Reference:  IsAssociativeElement)  set  whenever  the elements in the
        underlying  magma  and  in the coefficients ring have this filter set.
        [Reported by Randy Cone]
  
      The  function  InstallValue (Reference: InstallValue) must not be used
        for  objects in the filter IsFamily because these objects are compared
        via  IsIdenticalObj  (Reference:  IsIdenticalObj).  [Reported  by  Max
        Neunhöffer]
  
  Fixed bugs which could lead to crashes:
  
      Problem in composition series for permutation groups for non-Frobenius
        groups with regular point stabilizer.
  
      After   lots   of  computations  with  compressed  GF(2)  vectors  GAP
        occasionally  crashed.  The  reason were three missing CHANGED_BAGs in
        SemiEchelonPListGF2Vecs.   They   were   missing,  because  a  garbage
        collection  could  be triggered during the computation such that newly
        created bags could become old. It is not possible to provide test code
        because  the error condition cannot easily be reproduced. [Reported by
        Klaus Lux]
  
      Minor  bug  that  crashed  GAP:  The type of IMPLICATIONS could not be
        determined in a fresh session. [Reported by Marco Costantini]
  
      Assert  (Reference:  Assert)  caused an infinite loop if called as the
        first line of a function called from another function.
  
  Other fixed bugs:
  
      Wrong choice of prime in Dixon-Schneider if prime is bigger than group
        order (if group has large exponent).
  
      Groebner   basis  code  ran  into  problems  when  comparing  monomial
        orderings.
  
      When  testing  for  conjugacy  of  a primitive group to an imprimitive
        group,GAP  runs  into an error in EARNS calculation. [Reported by John
        Jones]
  
      The  centre  of  a magma is commonly defined to be the set of elements
        that  commute and associate with all elements. The previous definition
        left   out   associate   and   caused   problems  with  extending  the
        functionality to nonassociative loops. [Reported by Petr Vojtechovsky]
  
      New  kernel methods for taking the intersection and difference between
        sets of substantially different sizes give a big performance increase.
  
      The         commands        IsNaturalSymmetricGroup        (Reference:
        IsNaturalSymmetricGroup)   and  IsNaturalAlternatingGroup  (Reference:
        IsNaturalAlternatingGroup)  are  faster and should run much less often
        into inefficient tests.
  
      The  perfect  group  library,  see  Finite  Perfect Groups (Reference:
        Finite  Perfect  Groups), is split into several files which are loaded
        and unloaded to keep memory usage down. The global variable PERFSELECT
        is  a  blist  which  indicates  which  orders are currently loaded. An
        off-by-one  error  wrongly  added  the last order of the previous file
        into the list of valid orders when a new file was loaded. A subsequent
        access to this order raises an error.
  
      Up  to  now,  the  method  installed  for  testing  the  membership of
        rationals  in  the field of rationals via IsRat (Reference: IsRat) was
        not  called;  instead  a  more  general  method  was  used that called
        Conductor  (Reference:  Conductor  for a cyclotomic) and thus was much
        slower.  Now  the  special  method  has been ranked up by changing the
        requirements in the method installation.
  
      Fixed  a  bug  in APPEND_VEC8BIT, which was triggered in the following
        situation:  Let  e be the number of field elements stored in one byte.
        If  a  compressed  8bit-vector  v  had  length  not divisible by e and
        another  compressed  8-bit vector w was appended, such that the sum of
        the  lengths  became  divisible  by  e,  then  one 0 byte too much was
        written,  which  destroyed  the TNUM of the next GAP object in memory.
        [Reported by Klaus Lux]
  
      PermutationCycle  (Reference:  PermutationCycle)  returned fail if the
        cycle  was  not a contiguous subset of the specified domain. [Reported
        by Luc Teirlinck]
  
      Now  Inverse  (Reference: Inverse) correctly returns fail for zeros in
        finite fields (and does no longer enter a break loop).
  
      Up  to now, CharacterDegrees (Reference: CharacterDegrees) ignored the
        attribute  Irr  (Reference: Irr) if the argument was a group that knew
        that it was solvable.
  
      The  function  Debug now prints a meaningful message if the user tries
        to  debug an operation. Also, the help file for vi is now available in
        the case of several GAP root directories.
  
      It  is  no  longer  possible  to  create corrupt objects via ranges of
        length  >2^28,  resp.  >2^60  (depending  on  the  architecture).  The
        limitation concerning the arguments of ranges is documented. [Reported
        by Stefan Kohl]
  
      Now    IsElementaryAbelian    (Reference:   IsElementaryAbelian)   and
        ClassPositionsOfMinimalNormalSubgroups                     (Reference:
        ClassPositionsOfMinimalNormalSubgroups)  are  available  for  ordinary
        character    tables.   Now   the   operation   CharacterTableIsoclinic
        (Reference:  CharacterTableIsoclinic)  is  an  attribute, and there is
        another     new     attribute    SourceOfIsoclinicTable    (Reference:
        SourceOfIsoclinicTable)  that  points back to the original table; this
        is  used  for  computing  the  Brauer  tables  of  those tables in the
        character     table     library     that     are     computed    using
        CharacterTableIsoclinic.      Now      ClassPositionsOfDerivedSubgroup
        (Reference:   ClassPositionsOfDerivedSubgroup)   avoids   calling  Irr
        (Reference: Irr), since LinearCharacters (Reference: LinearCharacters)
        is sufficient. Now ClassPositionsOfElementaryAbelianSeries (Reference:
        ClassPositionsOfElementaryAbelianSeries)  works  also for the table of
        the  trivial  group.  Restrictions of character objects know that they
        are characters.
  
        A  few  formulations  in the documentation concerning character tables
        have been improved slightly.
  
      Up  to  now,  IsPGroup  (Reference: IsPGroup) has rarely been set. Now
        many basic operations such as SylowSubgroup (Reference: SylowSubgroup)
        set this attribute on the returned result.
  
      Computing an enumerator for a semigroup required too much time because
        it  used  all  elements  instead of the given generators. [Reported by
        Manuel Delgado]
  
      Avoid potential error message when working with automorphism groups.
  
      Fixed wrong page references in manual indices.
  
      Make MutableCopyMat an operation and install the former function which
        does  call  List  (Reference: list element operation) with ShallowCopy
        (Reference:  ShallowCopy)  the default method for lists. Also use this
        in a few appropriate places.
  
      An  old  DEC  compiler doesn't like C preprocessor directives that are
        preceded  by  whitespace.  Removed such whitespace. [Reported by Chris
        Wensley]
  
  New or improved functionality:
  
      The primitive groups library has been extended to degree 2499.
  
      New operation Remove (Reference: Remove) and extended functionality of
        Add  (Reference: Add) with an optional argument giving the position of
        the  insertion.  They  are  based  on  an  efficient  kernel  function
        COPY_LIST_ENTRIES.
  
      Added  fast  kernel  implementation of Tarjan's algorithm for strongly
        connected components of a directed graph.
  
      Now  IsProbablyPrimeInt  (Reference:  IsProbablyPrimeInt)  can be used
        with    larger    numbers.    (Made   internal   function   TraceModQF
        non-recursive.)
  
      A  new  operation  PadicValuation  (Reference:  PadicValuation)  and a
        corresponding method for rationals.
  
      A new operation PartialFactorization (Reference: PartialFactorization)
        has  been  added,  and  a  corresponding  method for integers has been
        installed.  This method allows one to specify the amount of work to be
        spent on looking for factors.
  
      The generators of full s. c. algebras can now be accessed with the dot
        operator. [Reported by Marcus Bishop]
  
      New  Conway  polynomials  computed  by Kate Minola, John Bray, Richard
        Parker.
  
      A      new      attribute     EpimorphismFromFreeGroup     (Reference:
        EpimorphismFromFreeGroup).  The  code  has  been  written by Alexander
        Hulpke.
  
      The  functions Lambda (Reference: Lambda), Phi (Reference: Phi), Sigma
        (Reference:  Sigma),  and  Tau  (Reference: Tau) have been turned into
        operations,  to  admit the installation of methods for arguments other
        than integers.
  
      Up  to  now,  one  could  assign only lists with InstallFlushableValue
        (Reference: InstallFlushableValue). Now also records are admitted.
  
      InstallMethod (Reference: InstallMethod) now admits entering a list of
        strings  instead  of a list of required filters. Each such string must
        evaluate  to  a  filter  when  used  as  the  argument  of  EvalString
        (Reference:  EvalString).  The advantage of this variant is that these
        strings  are  used  to  compose  an  info  string  (which  is shown by
        ApplicableMethod) that reflects exactly the required filters.
  
      In  test files that are read with ReadTest, the assertion level is set
        to 2 between START_TEST and STOP_TEST. This may result in runtimes for
        the  tests  that are substantially longer than the usual runtimes with
        default  assertion  level 0. In particular this is the reason why some
        of  the standard test files require more time in GAP 4.4.6 than in GAP
        4.4.5.
  
      Some very basic functionality for floats.
  
  
  8.7 GAP 4.4 Update 7 (March 2006)
  
  New or improved functionality:
  
      The  Display  (Reference:  Display) functionality for character tables
        has  been  extended  by  addition  of an option to show power maps and
        centralizer  orders  in  a  format  similar to that used in the ATLAS.
        Furthermore  the  options  handling  is  now hierarchical, in order to
        admit more flexible overloading.
  
      For      the     function     LowIndexSubgroupsFpGroup     (Reference:
        LowIndexSubgroupsFpGroup),   there   is   now   an   iterator  variant
        LowIndexSubgroupsFpGroupIterator.   [Suggested   (and  based  on  code
        contributed) by Michael Hartley]
  
      Semigroup functionality in GAP has been improved and extended. Green's
        relations  are now stored differently, making the system more amenable
        to  new  methods for computing these relations in special cases. It is
        now  possible  to calculate Green's classes etc. without computing the
        entire   semigroup   or   necessarily   loading  the  package  MONOID.
        Furthermore,  the  Froidure-Pin  algorithm has now been implemented in
        GAP.
  
      Functionality  for  creating  free  products of any list of groups for
        which  a  finite  presentation  can be determined had been added. This
        function  returns  a  finitely  presented  group.  This  functionality
        includes the Embedding operation. As an application of this new code a
        specialized  direct  product  operation  has  been  added for finitely
        presented  groups  which  returns  a  finitely  presented  group. This
        application includes Embedding and Projection functionality.
  
      Some new Straight Line Program (SLP) functionality has been added. The
        new  functions take given SLPs and create new ones by restricting to a
        subset  of the results, or to an intermediate result or by calculating
        the product of the results of two SLPs.
  
      New  code has been added to allow group elements with memory; that is,
        they  store automatically how they were derived from some given set of
        generators.  Note  that  there  is  not  yet  documentation  for  this
        functionality, but some packages already use it.
  
      New  code  has been added to handle matrices and vectors in such a way
        that they do not change their representation in a generic manner.
  
      The Irr (Reference: Irr) method for p-solvable p-modular Brauer tables
        now keeps the order of the irreducibles in the ordinary table.
  
      GAP can now handle any finite field for which the Conway polynomial is
        known or can be computed.
  
      New Conway polynomials provided by John Bray and Kate Minola have been
        added.
  
      The   ReadTest   methods  for  strings  (filenames)  and  streams  now
        automatically   set  the  screen  width  (see  SizeScreen  (Reference:
        SizeScreen)) to 80 before the tests, and reset it afterwards.
  
      Now a few more checks are done during the configure phase of compiling
        for  future  use  of some I/O functions of the C-library in a package.
        Also  the path to the GAP binaries for the GAP compiler is now handled
        via autoconf. Finally, now autoconf version 2.59 is used.
  
  Fixed bugs which could produce wrong results:
  
      Some  technical  errors  in  the  functions for compressed vectors and
        matrices  which  could  lead to corruption of internal data structures
        and  so to crashes or conceivably to wrong results. [Reported by Roman
        Schmied]
  
      A  potential  problem  in  the  generic  method  for  the undocumented
        operation   DirectFactorsOfGroup:   It   was   silently  assumed  that
        NormalSubgroups  (Reference:  NormalSubgroups)  delivers  the  trivial
        subgroup  as  first and the whole group as last entry of the resulting
        list.
  
      The  code for sublists of compressed vectors created by vec{range} may
        write  one  byte  beyond  the  space  allocated  for  the  new vector,
        overwriting  part  of the next object in the workspace. Thanks to Jack
        Schmidt for narrowing down the problem.
  
      Given  a class function object of value zero, an Arithmetic Operations
        for  Class  Functions  (Reference:  Arithmetic  Operations  for  Class
        Functions)  method  for  a  class  function erroneously did not return
        fail. [Reported by Jack Schmidt]
  
      The  Arithmetic  Operations for Class Functions (Reference: Arithmetic
        Operations   for   Class   Functions)  method  for  a  class  function
        erroneously returned a finite number if one of the values was nonreal,
        not a cyclotomic integer, and had norm 1.
  
      Two  missing  perfect  groups  were  added, and the permutation degree
        lowered  on  the perfect groups with the largest degrees. [Reported by
        Jack Schmidt]
  
      When  a  character  table was displayed with Printing Character Tables
        (Reference:   Printing   Character   Tables),  the  centralizer  order
        displayed  for  the  first  class  shown was not correct if it did not
        involve all prime divisors of the group. [Reported by Jack Schmidt]
  
      The   first   argument   of   the   function  VectorSpace  (Reference:
        VectorSpace)  must  be a field. This is checked from now on. [Reported
        by Laurent Bartholdi]
  
      Up  to  now, it was possible to create a group object from a semigroup
        of  cyclotomics using AsGroup (Reference: AsGroup), although groups of
        cyclotomics are not admissible. [Reported by Alexander Konovalov]
  
      The  documentation of CharacteristicPolynomial(F,mat) was ambiguous if
        FieldOfMatrix(mat)  <=  F  < DefaultFieldOfMatrix(mat). In particular,
        the result was representation dependent. This was fixed by introducing
        a  second  field which specifies the vector space which mat acts upon.
        [Reported by Jack Schmidt]
  
      AssociatedReesMatrixSemigroupOfDClass  produced  an incorrect sandwich
        matrix for the semigroup created. This matrix is an attribute set when
        creating  the  Rees  matrix semigroup but is not used for creating the
        semigroup.  The  incorrect result was returned when SandwichMatrix was
        called. [Reported by Nelson Silva and Joao Araujo]
  
      The  literal  "compiled" was given an incorrect length. The kernel was
        then  unable  to  find  compiled  library  code as the search path was
        incorrect.  Also  the  documentation  example had an error in the path
        used to invoke the gac compiler.
  
      The  twisting  group  in  a  generic  wreath  product  might  have had
        intransitive action. [Reported by Laurent Bartholdi]
  
      There was an arithmetic bug in the polynomial reduction code.
  
  Fixed bugs which could lead to crashes:
  
      Bug  1  in  the  list  of fixed bugs which could lead to wrong results
        could also potentially lead to crashes.
  
  Other fixed bugs:
  
      The  matrices  of  invariant  forms stored as values of the attributes
        InvariantBilinearForm        (Reference:       InvariantBilinearForm),
        InvariantQuadraticForm    (Reference:   InvariantQuadraticForm),   and
        InvariantSesquilinearForm  (Reference: InvariantSesquilinearForm), for
        matrix  groups  over finite fields, are now in the (compressed) format
        returned by ImmutableMatrix (Reference: ImmutableMatrix).
  
      String  now  returns  an  immutable  string,  by  making a copy before
        changing the argument.
  
      permutation^0  and permutation^1 were not handled with special code in
        the  kernel,  hence  were very slow for big permutations. [Reported by
        Max Neunhöffer]
  
      Added  code  to  cache  the induced pcgs for an arbitrary parent pcgs.
        (This code was formerly part of the CRISP package.)
  
      This  fix  consists  of numerous changes to improve support for direct
        products,  including:  -  new methods for PcgsElementaryAbelianSeries,
        PcgsChiefSeries,  ExponentsOfPcElement,  DepthOfPcElement  for  direct
        products  -  fixed EnumeratorOfPcgs to test for membership first - new
        methods  for  membership  test  in groups which have an induced pcgs -
        added  GroupOfPcgs  attribute  to  pcgs  in  various  methods  - fixed
        declarations   of  PcgsElementaryAbelianSeries,  PcgsChiefSeries  (the
        declared argument was a pcgs, not a group) [Reported by Roman Schmied]
  
      Corrected   a   term   ordering   problem  encountered  by  the  basis
        construction code for finite dimensional vector spaces of multivariate
        rational functions. [Reported by Jan Draisma]
  
      When  the  factor  of  a finite dimensional group ring by an ideal was
        formed, a method intended for free algebras modulo relations was used,
        and  the  returned  factor algebra could be used for (almost) nothing.
        [Reported by Heiko Dietrich]
  
      Up  to  now, PowerMap (Reference: PowerMap) ran into an error when one
        asked  for  the  n-th  power map where n was not a small integer. This
        happened  in  some  GAP  library  functions  if  the  exponent  of the
        character table in question was not a small integer.
  
      Up  to now, the test whether a finite field element was contained in a
        group  of  finite  field elements ran into an error if the element was
        not  in  the field generated by the group elements. [Reported by Heiko
        Dietrich]
  
      Conjugacy  classes  of  natural (special) linear groups are now always
        returned with trivial class first.
  
      Up   to   now,  it  could  happen  that  CheckFixedPoints  (Reference:
        CheckFixedPoints)  reduced  an  entry in its second argument to a list
        containing  only  one  integer  but  did  not replace the list by that
        integer;  according  to  the  conventions,  this replacement should be
        done.
  
      The functions PrintTo and AppendTo did not work correctly for streams.
        [Reported by Marco Costantini]
  
      The  function Basis did not return a value when it was called with the
        argument Rationals. [Reported by Klaus Lux]
  
      For certain matrix groups, the function StructureDescription raised an
        error  message.  The  reason  for  this  was that a trivial method for
        IsGeneralLinearGroup  for  matrix  groups  in  lib/grpmat.gi  which is
        ranked  higher  than  the  nontrivial  method  for  generic  groups in
        lib/grpnames.gi  called the operation IsNaturalGL, for which there was
        no nontrivial method available. [Reported by Nilo de Roock]
  
      Action  on  sets  of  length 1 was not correctly handled. [Reported by
        Mathieu Dutour]
  
      Now WriteByte admits writing zero characters to all streams. [Reported
        by Marco Costantini]
  
      The  conjugacy test for subgroups tests for elementary abelian regular
        normal subgroup (EARNS) conjugacy. The fix will catch this in the case
        that the second group has no EARNS. [Reported by Andrew Johnson]
  
      So far, the UNIX installation didn't result in a correct gap.sh if the
        installation  path  contained  space  characters. Now it should handle
        this case correctly, as well as other unusual characters in path names
        (except for double quotes).
  
  
  8.8 GAP 4.4 Update 8 (September 2006)
  
  New or improved functionality:
  
      A  function Positions (Reference: Positions) with underlying operation
        PositionsOp,  which returns the list of all positions at which a given
        object appears in a given list.
  
      LogFFE  (Reference: LogFFE) now returns fail when the element is not a
        power of the base.
  
      It is now allowed to continue long integers, strings or identifiers by
        ending a line with a backslash or with a backslash and carriage return
        character.  So,  files with GAP code and DOS/Windows-style line breaks
        are now valid input on all architectures.
  
      The  command  line for starting the session and the system environment
        are     now     available     in     GAPInfo.SystemCommandLine     and
        GAPInfo.SystemEnvironment.
  
      Names  of  all  bound  global  variables  and  all component names are
        available on GAP level.
  
      Added  a  few  new Conway polynomials computed by Kate Minola and John
        Bray.
  
      There   is  a  new  concept  of  random  sources,  see  IsRandomSource
        (Reference:  IsRandomSource),  which provides random number generators
        which  are  independent  of  each  other. There is kernel code for the
        Mersenne  twister random number generator (based on the code by Makoto
        Matsumoto                        distributed                        at
        http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html). It provides
        fast  32-bit  pseudorandom  integers with a period of length 2^19937-1
        and a 623-dimensional equidistribution. The library methods for random
        elements  of  lists  and  for  random  (long)  integers  are using the
        Mersenne twister now.
  
      In  line  editing  mode  (usual input mode without -n option) in lines
        starting  with  gap>  , >  or brk>  this beginning part is immediately
        removed. This is a convenient feature that allows one to cut and paste
        input  lines  from  other  sessions  or  from manual examples into the
        current session.
  
  Fixed bugs which could produce wrong results:
  
      The   function   Decomposition   (Reference:  Decomposition)  returned
        coefficient  vectors  also  in  certain  situations  where  in fact no
        decomposition  exists. This happened only if the matrix entered as the
        first  argument  contained  irrational  values and a row in the matrix
        entered as the second argument did not respect the algebraic conjugacy
        relations  between  the columns of the first argument. So there was no
        problem for the usual cases that the two matrices are integral or that
        they are lists of Brauer characters. [Reported by Jürgen Müller]
  
      PC  group  homomorphisms  can  claim a wrong kernel after composition.
        [Reported by Serge Bouc]
  
      The  return  value  of OctaveAlgebra (Reference: OctaveAlgebra) had an
        inconsistent  defining  structure  constants  table  for  the  case of
        coefficients  fields  not  containing  the  integer zero. [Reported by
        Gábor Nagy]
  
      The manual guarantees that a conjugator automorphism has a conjugating
        element in the group if possible. This was not guaranteed.
  
      StabChain  (Reference:  StabChain  for  a  group  (and  a record)) for
        symmetric  groups  gave a wrong result if fixed points were prescribed
        for base.
  
      Contrary  to  what  is documented the function POW_OBJ_INT returned an
        immutable  result for POW_OBJ_INT(m,1) for a mutable object m. This is
        triggered by the code m^1.
  
      PseudoRandom  (Reference:  PseudoRandom)  for a group had a problem if
        the  group  had  lots  of equal generators. The produced elements were
        extremely  poorly  distributed in that case. This is now fixed for the
        case that elements of the group can easily be sorted.
  
      Fixed  the bug that the type of a boolean list (see More about Boolean
        Lists (Reference: More about Boolean Lists)) was computed wrongly: The
        type previously had IS_PLIST_REP instead of IS_BLIST_REP in its filter
        list.
  
      Orbits (Reference: Orbits) did not respect a special PositionCanonical
        (Reference:   PositionCanonical)   method   for   right  transversals.
        [Reported by Steve Costenoble]
  
      Wrong  results for GcdInt (Reference: GcdInt) for some arguments on 64
        bit systems only. [Reported by Robert Morse]
  
      When  prescribing  a  subgroup to be included, the low index algorithm
        for   fp  groups  sometimes  returned  subgroups  which  are  in  fact
        conjugate. (No subgroups are missing.) [Reported by Ignaz Soroko]
  
  Fixed bugs which could lead to crashes:
  
      The  command  line  option  -x  allowed arguments > 256 which can then
        result  in  internal  buffers  overflowing.  Now bigger numbers in the
        argument are equivalent to -x 256. [Reported by Michael Hartley]
  
  Other fixed bugs:
  
      Two  special methods for the operation CompositionMapping2 (Reference:
        CompositionMapping2)  were  not  correct,  such  that  composing  (and
        multiplying)  certain  group  homomorphisms did not work. [Reported by
        Peter Mayr]
  
      In    the    definition    of    FrobeniusCharacterValue   (Reference:
        FrobeniusCharacterValue),  it  had  been  stated  erroneously that the
        value  must  lie  in  the  field of p^n-th roots of unity; the correct
        condition  is that the value must lie in the field of (p^n-1)-th roots
        of unity. [Reported by Jack Schmidt]
  
      The  function DirectProduct (Reference: DirectProduct) failed when one
        of the factors was known to be infinite.
  
      For  a  linear  action  homomorphism PreImageElm was very slow because
        there was no good method to check for injectivity, which is needed for
        nearly  all  good methods for PreImageElm. This change adds such a new
        method for IsInjective. [Reported by Akos Seress]
  
      Rare errors in the complement routine for permutation groups.
  
      Blocks  code  now  uses  jellyfish-style  random elements to avoid bad
        Schreier trees.
  
      A method for IsPolycyclicGroup (Reference: IsPolycyclicGroup) has been
        added. Such a method was missing so far.
  
      Corrected  EpimorphismSchurCover (Reference: EpimorphismSchurCover) to
        handle  the  trivial  group  correctly.  Added new methods that follow
        immediately  from  computing the Schur Cover of a group. The attribute
        Epicentre       (Reference:       Epicentre),      the      operations
        NonabelianExteriorSquare   (Reference:  NonabelianExteriorSquare)  and
        EpimorphismNonabelianExteriorSquare                        (Reference:
        EpimorphismNonabelianExteriorSquare), and the property IsCentralFactor
        (Reference:   IsCentralFactor)   are   added   to   the  library  with
        documentation and references.
  
      Display  the  correct expression in a call stack trace if an operation
        was  called  somewhere  up  due to the evaluation of a unary or binary
        operation.
  
      Made  StripMemory  an  operation  rather than a global function. Added
        ForgetMemory operation.
  
      Adjust   things   slightly   to   make   later   conversion   to   new
        vectors/matrices easier. Nothing of this should be visible.
  
      Corrected  some  details  in  the  documentation  of the GAP language.
        [Reported by Alexander Konovalov]
  
      Now  PositionSorted (Reference: PositionSorted) is much faster on long
        mutable  plain  lists.  (The  former  operation  is  substituted  by a
        function  and  a  new operation PositionSortedOp.) [Reported by Silviu
        Radu]
  
      Now  it  is possible to switch repeated warnings off when working with
        iterative polynomial rings.
  
  
  8.9 GAP 4.4 Update 9 (November 2006)
  
  Fixed bugs which could produce wrong results:
  
      The  methods  of ReadByte (Reference: ReadByte) for reading from files
        or  terminals  returned  wrong  results  for  characters  in the range
        [128..255]. [Reported by Yevgen Muntyan]
  
  Other fixed bugs:
  
      A  method for the operation PseudoRandom (Reference: PseudoRandom) did
        not succeed.
  
      A fix for Orbits with a set of points as a seed.
  
      Added  a  generic  method  such  that Positions (Reference: Positions)
        works with all types of lists.
  
      Fixed   a  problem  in  choosing  the  prime  in  the  Dixon-Schneider
        algorithm. [Reported by Toshio Sumi]
  
  New or improved functionality:
  
      ReducedOrdinary  was used in the manual, but was not documented, being
        a   synonym  for  the  documented  ReducedCharacters.  Changed  manual
        examples to use the latter form. [Reported by Vahid Dabbaghian]
  
  
  8.10 GAP 4.4 Update 10 (October 2007)
  
  New or improved functionality:
  
      Files in the cnf directory of the GAP distribution are now archived as
        binary files. Now GAP can be installed with UNIX or with WINDOWS style
        line breaks on any system and should work without problems.
  
      Since large finite fields are available, some restrictions in the code
        for  computing  irreducible  modules  over finite fields are no longer
        necessary.  (They  had  been  introduced in order to give better error
        messages.)
  
      Made PositionSublist faster in case the search string does not contain
        repetitive patterns.
  
      The function MakeImmutable now returns its argument.
  
      Dynamically  loaded  modules  now  work on Mac OS X. As a consequence,
        this allows to work with the Browse, EDIM and IO packages on Mac OS X.
  
      Introduced  ViewObj  and PrintObj methods for algebraic number fields.
        Made  them  applicable  to  AlgebraicExtension  by adding the property
        IsNumberField in the infinite field case.
  
      The  function CharacterTableRegular (Reference: CharacterTableRegular)
        is documented now.
  
      The  function  ScalarProduct (Reference: ScalarProduct for characters)
        now accepts also Brauer characters as arguments.
  
      The  function  QuaternionAlgebra  (Reference:  QuaternionAlgebra)  now
        accepts  also  a  list of field elements instead of a field. Also, now
        the  comparison of return values (w.r.t. equality, containment) yields
        true if the parameters coincide and the ground fields fit.
  
      The  function  RemoveCharacters  (Reference:  RemoveCharacters) is now
        documented.
  
      Lists  in GAP sometimes occupy memory for possible additional entries.
        Now plain lists and strings read by GAP and the lists returned by List
        (Reference: list element operation) only occupy the memory they really
        need.  For  more  details  see  the  documentation of the new function
        EmptyPlist (Reference: EmptyPlist).
  
      There  are  some  new  Conway  polynomials  in  characteristic 2 and 3
        provided by Kate Minola.
  
      A new operation MemoryUsage determines the memory usage in bytes of an
        object and all its subobjects. It does not consider families and types
        but handles arbitrary self-referential structures of objects.
  
  Fixed bugs which could produce wrong results:
  
      When  forming  the  semidirect product of a matrix group with a vector
        space  over a non-prime field the embedding of the vector space gave a
        wrong result. [Reported by anvita21]
  
      DefaultRing  failed  for  constant  polynomials  over nonprime fields.
        [Reported by Stefan Kohl]
  
      The method in ffeconway.gi that gets coefficients WRT to the canonical
        basis  of  the  field  from  the representation is only correct if the
        basis  is  over  the prime field. Added a TryNextMethod if this is not
        the case. [Reported by Alla Detinko]
  
      Creating  a  large  (>2^16)  field  over  a  non-prime  subfield  went
        completely wrong. [Reported by Jack Schmidt, from Alla Detinko]
  
      A method for Coefficients for Conway polynomial FFEs didn't check that
        the  basis  provided  was  the  canonical  basis  of  the RIGHT field.
        [Reported by Bettina Eick]
  
      An  elementary  abelian series was calculated wrongly. [Reported by N.
        Sieben]
  
      Orbits on sets of transformations failed.
  
      Wrong  methods  for GeneratorsOfRing (Reference: GeneratorsOfRing) and
        GeneratorsOfRingWithOne (Reference: GeneratorsOfRingWithOne) have been
        removed.  These  methods  were  based  on  the assumption that one can
        obtain  a set of ring generators by taking the union of a known set of
        field  generators,  the  set of the inverses of these field generators
        and {1}.
  
      The name of a group of order 117600 and degree 50 was incorrect in the
        Primitive  Permutation  Groups (primgrp: Primitive Permutation Groups)
        Primitive  Permutation  Groups  library.  In  particular,  a group was
        wrongly labelled as PGL(2, 49).
  
      There  was  a  possible error in SubgroupsSolvableGroup when computing
        subgroups within a subgroup.
  
      An error in 2-Cohomology computation for pc groups was fixed.
  
      IsConjugate used normality in a wrong supergroup
  
  Fixed bugs which could lead to crashes:
  
      GAP  crashed when the PATH environment variable was not set. [Reported
        by Robert F. Morse]
  
      GAP  could  crash  when  started  with  option -x 1. Now the number of
        columns is initialized with at least 2. [Reported by Robert F. Morse]
  
      After  loading a saved workspace GAP crashed when one tried to slice a
        compressed  vector  over a field with 2 < q <= 256 elements, which had
        already   existed   in  the  saved  workspace.  [Reported  by  Laurent
        Bartholdi]
  
      FFECONWAY.WriteOverSmallestCommonField  tripped  up  when  the  common
        field is smaller than the field over which some of the vector elements
        are written, because it did a test based on the degree of the element,
        not the field it is written over. [Reported by Thomas Breuer]
  
      Fixed  the  following  error:  When  an  FFE  in the Conway polynomial
        representation  actually  lied  in  a  field  that  is  handled in the
        internal  representation  (eg  GF(3)) and you tried to write it over a
        bigger  field  that  is  ALSO handled internally (eg GF(9)) you got an
        element  written  over  the larger field, but in the Conway polynomial
        representation, which is forbidden. [Reported by Jack Schmidt]
  
      Attempting  to compress a vector containing elements of a small finite
        field  represented  as  elements of a bigger (external) field caused a
        segfault. [Reported by Edmund Robertson]
  
      GAP  crashed  when  BlistList  was  called  with  a  range  and a list
        containing  large  integers  or  non-integers.  [Reported  by  Laurent
        Bartholdi]
  
      GAP  no  longer  crashes  when  OnTuples  is  called  with a list that
        contains holes. [Reported by Thomas Breuer]
  
  Other fixed bugs:
  
      Socle for the trivial group could produce an error message.
  
      DirectoryContents (Reference: DirectoryContents) ran into an error for
        immutable  strings  without  trailing  slash as argument. [Reported by
        Thomas Breuer]
  
      The  functions IsInjective (Reference: IsInjective) and IsSingleValued
        (Reference:  IsSingleValued)  did not work for general linear mappings
        with trivial (pre)image. [Reported by Alper Odabas]
  
      Creating an enumerator for a prime field with more than 65536 elements
        ran into an infinite recursion. [Reported by Akos Seress]
  
      The  performance  of  List,  Filtered,  Number,  ForAll  and ForAny if
        applied  to  non-internally  represented  lists was improved. Also the
        performance of iterators for lists was slightly improved.
  
      Finite  field  elements  now know that they can be sorted easily which
        improves performance in certain lookups.
  
      A  method  for IsSubset (Reference: IsSubset) was missing for the case
        that  exactly  one  argument  is  an  inhomogeneous list. [Reported by
        Laurent Bartholdi]
  
      Long   integers   in   expressions   are  now  printed  (was  not  yet
        implemented). [Reported by Thomas Breuer]
  
      Fixed kernel function for printing records.
  
      New C library interfaces (e.g., to ncurses in the Browse package) need
        some more memory to be allocated with malloc. The default value of GAP
        -a option is now 2m>.
  
      Avoid warnings about pointer types by newer gcc compilers.
  
      IsBound(l[pos])  was  failing  for a large integer pos only when coded
        (e.g. in a loop or function body).
  
      ZmodpZObj  is  now  a synonym for ZmodnZObj such that from now on such
        objects print in a way that can be read back into GAP.
  
      The outdated note that binary streams are not yet implemented has been
        removed.
  
  
  8.11 GAP 4.4 Update 11 (December 2008)
  
  Fixed bugs which could produce wrong results:
  
      MemoryUsage  (Reference:  MemoryUsage)  on  objects with no subobjects
        left  them  in  the  cache  and thus reported 0 in subsequent calls to
        MemoryUsage for the same object. [Reported by Stefan Kohl]
  
      Irr  (Reference:  Irr) might be missing characters. [Reported by Angel
        del Rio]
  
      Up    to    now,    it    was    allowed    to   call   the   function
        FullMatrixAlgebraCentralizer (Reference: FullMatrixAlgebraCentralizer)
        with  a  field  and  a  list  of matrices such that the entries of the
        matrices  were  not  contained  in  the  field; in this situation, the
        result  did  not  fit  to  the  documentation.  Now the entries of the
        matrices  are  required  to  lie in the field, if not then an error is
        signaled.
  
      For  those  finite  fields  that are regarded as field extensions over
        non-prime   fields   (one  can  construct  such  fields  with  AsField
        (Reference:  AsField)),  the  function  DefiningPolynomial (Reference:
        DefiningPolynomial)  erroneously  returned  a  polynomial  w.r.t.  the
        extension of the prime field. [Reported by Stefan Kohl]
  
      Since  the  release  of  GAP 4.4.10, the return values of the function
        QuaternionAlgebra  (Reference:  QuaternionAlgebra) were not consistent
        w.r.t.      the      attribute     GeneratorsOfAlgebra     (Reference:
        GeneratorsOfAlgebra);  the  returned  list  could  have length four or
        five.  Now  always  the  list  of  elements  of the canonical basis is
        returned.
  
      MonomialGrevlexOrdering      (Reference:      MonomialGrevlexOrdering)
        calculated a wrong ordering in certain cases. [Reported by Paul Smith]
  
      The  (GAP  kernel)  method  for the operation IntersectSet (Reference:
        IntersectSet)  for  ranges  had  two  bugs, which could yield a result
        range  with either too few or too many elements. As a consequence, for
        example  the Intersection (Reference: Intersection) results for ranges
        could be wrong. [Reported by Matthew Fayers]
  
      Fixed  a  bug  in  the short-form display of elements of larger finite
        fields,  a bug in some cross-field conversions and some inefficiencies
        and a missing method in the LogFFE (Reference: LogFFE) code. [Reported
        by Jia Huang]
  
      In    rare   cases   SmithNormalFormIntegerMatTransforms   (Reference:
        SmithNormalFormIntegerMatTransforms) returned a wrong normal form (the
        version without transforming matrices did not have this problem). This
        is fixed. [Reported by Alexander Hulpke]
  
      The   variant   of   the   function   StraightLineProgram  (Reference:
        StraightLineProgram   for   a   list  of  lines  (and  the  number  of
        generators))  that takes a string as its first argument returned wrong
        results if the last character of this string was a closing bracket.
  
      The  code  for  central series in a permutation group used too tight a
        bound  and  thus  falsely  return  a  nilpotent  permutation  group as
        non-nilpotent.
  
  Fixed bugs which could lead to crashes:
  
      Under  certain  circumstances  the  kernel code for position in blists
        would  access  a  memory  location just after the end of the blist. If
        this  location  was  not  accessible,  a  crash could result. This was
        corrected and the code was cleaned up. [Reported by Alexander Hulpke]
  
  Other fixed bugs:
  
      The    function    IsomorphismTypeInfoFiniteSimpleGroup    (Reference:
        IsomorphismTypeInfoFiniteSimpleGroup)  can  be  called with a positive
        integer  instead  of  a  group, and then returns information about the
        simple   group(s)   of   this   order.   (This  feature  is  currently
        undocumented.)  For  the  argument 1, however, it ran into an infinite
        loop.
  
      A  lookup  in  an  empty  dictionary entered a break loop. Now returns
        fail. [Reported by Laurent Bartholdi]
  
      The  c++ keyword and can no longer be used as a macro parameter in the
        kernel. [Reported by Paul Smith]
  
      The    operation    KernelOfMultiplicativeGeneralMapping   (Reference:
        KernelOfMultiplicativeGeneralMapping)  has  methods designed to handle
        maps  between  permutation  groups in a two-step approach, but did not
        reliably  trigger the second step. This has now been fixed, preventing
        a  slow infinite loop repeating the first step. This was normally only
        seen as part of a larger calculation.
  
      There  were  two  methods  for the operation Intersection2 (Reference:
        Intersection2)  which  have  implicitly  assumed  that finiteness of a
        collection  can  always  be  decided.  Now,  these  methods  check for
        IsFinite   (Reference:   IsFinite)   and   CanComputeSize  (Reference:
        CanComputeSize) prior to calling IsFinite (Reference: IsFinite).
  
      Made  error  message  in  case  of  corrupted  help  book  information
        (manual.six file) shorter and more informative. [Reported by Alexander
        Hulpke]
  
      GAP  cannot  call  methods  with  more  than  six  arguments.  Now the
        functions  NewOperation  (Reference:  NewOperation),  DeclareOperation
        (Reference:    DeclareOperation),    and   InstallMethod   (Reference:
        InstallMethod) signal an error if one attempts to declare an operation
        or to install a method with more than six arguments.
  
      Up  to  now, IsOne (Reference: IsOne) had a special method for general
        mappings,  which  was much worse than the generic method; this special
        method has now been removed.
  
      When  printing  elements  of an algebraic extension parentheses around
        coefficients were missing. [Reported by Maxim Hendriks]
  
  New or improved functionality:
  
      Make  dynamic  loading of modules possible on CYGWIN using a DLL based
        approach. Also move to using autoconf version 2.61.
  
      One  can  now  call  Basis  (Reference:  Basis),  Iterator (Reference:
        Iterator)    etc.    with   the   return   value   of   the   function
        AlgebraicExtension (Reference: AlgebraicExtension).
  
      The         function        FrobeniusCharacterValue        (Reference:
        FrobeniusCharacterValue)  returned  fail  for  results  that require a
        finite  field  with more than 65536 elements. Meanwhile GAP can handle
        larger  finite  fields,  so this restriction was removed. (It is still
        possible        that        FrobeniusCharacterValue        (Reference:
        FrobeniusCharacterValue) returns fail.)
  
      Methods  for  testing  membership in general linear groups and special
        linear groups over the integers have been added.
  
      Methods  for  String  (Reference:  String) and ViewString for full row
        modules  have  been  added.  Further, a default method for IsRowModule
        (Reference:  IsRowModule)  has  been  added,  which  returns false for
        objects which are not free left modules.
  
      A ViewString method for objects with name has been added.
  
      The  method  for  View (Reference: View) for polynomial rings has been
        improved,  and  methods  for String (Reference: String) and ViewString
        for polynomial rings have been added.
  
      Binomial (Reference: Binomial) now works with huge n.
  
      The      function     InducedClassFunctionsByFusionMap     (Reference:
        InducedClassFunctionsByFusionMap) is now documented.
  
      The  return  values  of  the  function  QuaternionAlgebra  (Reference:
        QuaternionAlgebra) now store that they are division rings (if optional
        parameters are given then of course ths depends on these parameters).
  
  
  8.12 GAP 4.4 Update 12 (December 2008)
  
  Fixed bugs which could lead to crashes:
  
      A  bug whereby leaving an incomplete statement on a line (for instance
        typing  while  and then return) when prompt colouring was in use could
        lead to GAP crashing.
  
  Other fixed bugs:
  
      A  bug which made the command-line editor unusable in a 64-bit version
        of GAP on Mac OS X.