  
  [1X2 [33X[0;0YChanges between [5XGAP[105X[101X[1X 4.6 and [5XGAP[105X[101X[1X 4.7[133X[101X
  
  [33X[0;0YThis  chapter  contains  an overview of most important changes introduced in
  [5XGAP[105X  4.7.2  release  (the first public release of [5XGAP[105X 4.7). It also contains
  information about subsequent update releases for [5XGAP[105X 4.7.[133X
  
  
  [1X2.1 [33X[0;0Y[5XGAP[105X[101X[1X 4.7.2 (December 2013)[133X[101X
  
  
  [1X2.1-1 [33X[0;0YChanges in the core [5XGAP[105X[101X[1X system introduced in [5XGAP[105X[101X[1X 4.7[133X[101X
  
  [33X[0;0YImproved and extended functionality:[133X
  
  [30X    [33X[0;6YThe methods for computing conjugacy classes of permutation groups have
        been  rewritten  from  scratch  to  enable potential use for groups in
        different  representations.  As  a  byproduct  the  resulting  code is
        (sometimes  notably)  faster.  It  also  now  is possible to calculate
        canonical conjugacy class representatives in permutation groups, which
        can be beneficial when calculating character tables.[133X
  
  [30X    [33X[0;6YThe  methods  for  determining  (conjugacy  classes  of)  subgroups in
        non-solvable  groups  have  been  substantially  improved in speed and
        scope for groups with multiple nonabelian composition factors.[133X
  
  [30X    [33X[0;6YThere  is  a  new  method  for  calculating the maximal subgroups of a
        permutation  group  (with  chief  factors  of  width  less or equal 5)
        without calculating the whole subgroup lattice.[133X
  
  [30X    [33X[0;6YIf  available,  information from the table of marks library is used to
        speed up subgroup calculations in almost simple factor groups.[133X
  
  [30X    [33X[0;6YThe  broader  availability of maximal subgroups is used to improve the
        calculation of double cosets.[133X
  
  [30X    [33X[0;6YTo  illustrate  the  improvements  listed  above,  one  could try, for
        example[133X
  
  [4X      [32X  Example  [32X[104X
          [4X[28Xg:=WreathProduct(MathieuGroup(11),Group((1,2)));[128X[104X
          [4X[28XLength(ConjugacyClassesSubgroups(g));[128X[104X
        [4X[32X[104X
  
        [33X[0;6Yand[133X
  
  [4X      [32X  Example  [32X[104X
          [4X[28Xg:=SemidirectProduct(GL(3,5),GF(5)^3);[128X[104X
          [4X[28Xg:=Image(IsomorphismPermGroup(g));[128X[104X
          [4X[28XMaximalSubgroupClassReps(g);[128X[104X
        [4X[32X[104X
  
  [30X    [33X[0;6YComputing  the  exponent  of a finite group [22XG[122X could be extremely slow.
        This  was  due to a slow default method being used, which computed all
        conjugacy classes of elements in order to compute the exponent. We now
        instead  compute Sylow subgroups [22XP_1[122X, ..., [22XP_k[122X of [22XG[122X and use the easily
        verified  equality [22Xexp(G) = exp(P_1) x ... x exp(P_k)[122X. This is usually
        at least as fast and in many cases orders of magnitude faster.[133X
  
  [4X      [32X  Example  [32X[104X
          [4X[25Xgap>[125X [27XG:=SmallGroup(2^7*9,33);;[127X[104X
          [4X[25Xgap>[125X [27XH:=DirectProduct(G, ElementaryAbelianGroup(2^10));;[127X[104X
          [4X[25Xgap>[125X [27XExponent(H); # should take at most a few milliseconds[127X[104X
          [4X[28X72[128X[104X
          [4X[25Xgap>[125X [27XK := PerfectGroup(2688,3);;[127X[104X
          [4X[25Xgap>[125X [27XExponent(K); # should take at most a few seconds[127X[104X
          [4X[28X168[128X[104X
        [4X[32X[104X
  
  [30X    [33X[0;6YThe  functionality  in  [5XGAP[105X  for  transformations  and  transformation
        semigroups  has  been rewritten and extended. Partial permutations and
        inverse  semigroups have been newly implemented. The documentation for
        transformations  and  transformation  semigroups  has  been  improved.
        Transformations  and  partial  permutations are implemented in the [5XGAP[105X
        kernel.  Methods  for  calculating  attributes  of transformations and
        partial permutations, and taking products, and so are also implemented
        in   the   kernel.  The  new  implementations  are  largely  backwards
        compatible; some exceptions are given below.[133X
  
        [33X[0;6YThe  degree  of  a  transformation [10Xf[110X is usually defined as the largest
        positive  integer  where  [10Xf[110X  is  defined. In previous versions of [5XGAP[105X,
        transformations were only defined on positive integers less than their
        degree,  it  was  only  possible  to multiply transformations of equal
        degree,  and  a  transformation did not act on any point exceeding its
        degree.  Starting  with  [5XGAP[105X  4.7,  transformations  behave  more like
        permutations,  in  that they fix unspecified points and it is possible
        to multiply arbitrary transformations.[133X
  
        [30X    [33X[0;12Yin  the  display  of a transformation, the trailing fixed points
              are  no  longer  printed.  More  precisely,  in the display of a
              transformation  [10Xf[110X  if [10Xn[110X is the largest value such that [10Xn^f<>n[110X or
              [10Xi^f=n[110X  for  some  [10Xi<>n[110X,  then  the  values  exceeding  [10Xn[110X are not
              printed.[133X
  
        [30X    [33X[0;12Ythe  display for semigroups of transformations now includes more
              information,  for  example  [10X<transformation  semigroup on 10 pts
              with  10  generators>[110X  and [10X<inverse partial perm semigroup on 10
              pts with 10 generators>[110X.[133X
  
        [30X    [33X[0;12Ytransformations  which define a permutation can be inverted, and
              groups of transformations can be created.[133X
  
        [33X[0;6YFurther    information    regarding    transformations   and   partial
        permutations,  can  be found in the relevant chapters of the reference
        manual.[133X
  
        [33X[0;6YThe  code  for Rees matrix semigroups has been completely rewritten to
        fix  the numerous bugs in the previous versions. The display of a Rees
        matrix semigroup has also been improved to include the numbers of rows
        and   columns,   and   the   underlying   semigroup.   Again  the  new
        implementations should be backwards compatible with the exception that
        the display is different.[133X
  
        [33X[0;6YThe  code for magmas with a zero adjoined has been improved so that it
        is  possible  to access more information about the original magma. The
        display  has also been changed to indicate that the created magma is a
        magma  with zero adjoined (incorporating the display of the underlying
        magma).  Elements  of a magma with zero are also printed so that it is
        clear that they belong to a magma with zero.[133X
  
        [33X[0;6YIf   a   semigroup   is   created   by   generators  in  the  category
        IsMultiplicativeElementWithOneCollection and CanEasilyCompareElements,
        then  it  is  now  checked  if the One of the generators is given as a
        generator. In this case, the semigroup is created as a monoid.[133X
  
  [30X    [33X[0;6YAdded    a    new    operation    [2XGrowthFunctionOfGroup[102X    ([14XReference:
        GrowthFunctionOfGroup[114X)  that  gives  sizes  of distance spheres in the
        Cayley graph of a group.[133X
  
  [30X    [33X[0;6YA new group constructor [2XFreeAbelianGroup[102X ([14XReference: FreeAbelianGroup[114X)
        for  free  abelian  groups  has  been  added.  By  default, it creates
        suitable  fp  groups.  Though  free abelian groups groups do not offer
        much  functionality right now, in the future other implementations may
        be provided, e.g. by the [5XPolycyclic[105X package.[133X
  
  [30X    [33X[0;6YThe  message about halving the pool size at startup is only shown when
        [10X-D[110X   command  line  option  is  used  (see  [14X'Reference:  Command  Line
        Options'[114X). [Suggested by Volker Braun][133X
  
  [30X    [33X[0;6YAn  info  class called [2XInfoObsolete[102X ([14XReference: InfoObsolete[114X) with the
        default  level  0 is introduced. Setting it to 1 will trigger warnings
        at     runtime    if    an    obsolete    variable    declared    with
        [10XDeclareObsoleteSynonym[110X  is  used.  This is recommended for testing [5XGAP[105X
        distribution and packages.[133X
  
  [30X    [33X[0;6YThe  [5XGAP[105X  help  system  now  recognises some common different spelling
        patterns (for example, -ise/-ize, -isation/-ization, solvable/soluble)
        and  searches for all possible spelling options even when the synonyms
        are not declared.[133X
  
  [30X    [33X[0;6YAdded  new  function  [2XCite[102X  ([14XReference:  Cite[114X) which produces citation
        samples for [5XGAP[105X and packages.[133X
  
  [30X    [33X[0;6YIt  is now possible to compile [5XGAP[105X with user-supplied [10XCFLAGS[110X which now
        will  not be overwritten by [5XGAP[105X default settings. [Suggested by Jeroen
        Demeyer][133X
  
  [33X[0;0YFixed bugs:[133X
  
  [30X    [33X[0;6Y[2XUnion[102X  ([14XReference:  Union[114X) had [22XO(n^3)[122X behaviour when given many ranges
        (e.g.  it  could  take  10  seconds  to find a union of 1000 1-element
        sets).  The new implementation reduces that to [22XO(n log n)[122X (and 4ms for
        the  10  second example), at the cost of not merging ranges as well as
        before in some rare cases.[133X
  
  [30X    [33X[0;6Y[10XIsLatticeOrderBinaryRelation[110X  only  checked  the  existence  of  upper
        bounds but not the uniqueness of the least upper bound (and dually for
        lower  bounds),  so  in  some  cases it could return the wrong answer.
        [Reported by Attila Egri-Nagy][133X
  
  [30X    [33X[0;6Y[2XLowIndexSubgroupsFpGroup[102X     ([14XReference:     LowIndexSubgroupsFpGroup[114X)
        triggered  a  break loop if the list of generators of the 2nd argument
        contained  the  identity  element  of  the  group.  [Reported by Ignat
        Soroko][133X
  
  [30X    [33X[0;6YFixed        regression        in       heuristics       used       by
        [2XNaturalHomomorphismByNormalSubgroup[102X                        ([14XReference:
        NaturalHomomorphismByNormalSubgroup[114X)  that could produce a permutation
        representation  of  an  unreasonably  large degree. [Reported by Izumi
        Miyamoto][133X
  
  [30X    [33X[0;6YFixed  inconsistent  behaviour  of [10XQuotientMod( Integers, r, s, m )[110X in
        the  case  where  [3Xs[103X  and [3Xm[103X are not coprime. This fix also corrects the
        division  behaviour  of  [10XZmodnZ[110X  objects,  see [2XQuotientMod[102X ([14XReference:
        QuotientMod[114X)   and  [2XZmodnZ[102X  ([14XReference:  ZmodnZ[114X).  [Reported  by  Mark
        Dickinson][133X
  
  [30X    [33X[0;6YFixed  an  oversight in the loading process causing [2XOnQuit[102X ([14XReference:
        OnQuit[114X) not resetting the options stack after exiting the break loop.[133X
  
  [30X    [33X[0;6YEmpty  strings were treated slightly differently than other strings in
        the  [5XGAP[105X  kernel,  for  historical  reasons.  This resulted in various
        inconsistencies.  For  example,  [10XIsStringRep("")[110X  returned true, but a
        method  installed  for  arguments  of  type  [10XIsStringRep[110X  would NOT be
        invoked when called with an empty string.[133X
  
        [33X[0;6YWe  remove  this  special case in the [5XGAP[105X kernel (which dates back the
        very  early  days  of  [5XGAP[105X 4 in 1996). This uncovered one issue in the
        kernel  function  [10XPOSITION_SUBSTRING[110X  (when  calling  it with an empty
        string as second argument), which was also fixed.[133X
  
  [30X    [33X[0;6YThe parser for floating point numbers contained a bug that could cause
        [5XGAP[105X  to crash or to get into a state where the only action left to the
        user  was to exit [5XGAP[105X via Ctrl-D. For example, entering four dots with
        spaces between them on the [5XGAP[105X prompt and then pressing the return key
        caused [5XGAP[105X to exit.[133X
  
        [33X[0;6YThe reason was (ironically) an error check in the innards of the float
        parser code which invoked the [5XGAP[105X [10XError()[110X function at a point where it
        should not have.[133X
  
  [30X    [33X[0;6YRemoving  the last character in a string was supposed to overwrite the
        old  removed character in memory with a zero byte, but failed to do so
        due  to  an  off-by-one  error.  For  most [5XGAP[105X operations, this has no
        visible  effect,  except  for  those  which  directly  operate  on the
        underlying  memory representation of strings. For example, when trying
        to  use  such  a string to reference a record entry, a (strange) error
        could be triggered.[133X
  
  [30X    [33X[0;6Y[2XViewString[102X   ([14XReference:  ViewString[114X)  and  [2XDisplayString[102X  ([14XReference:
        DisplayString[114X) are now handling strings, characters and immediate FFEs
        in a consistent manner.[133X
  
  [30X    [33X[0;6YMultiple  fixes  to the build process for less common Debian platforms
        (arm, ia64, mips, sparc, GNU/Hurd). [Suggested by Bill Allombert][133X
  
  [30X    [33X[0;6YFixes  for  several  regressions in the [11Xgac[111X script. [Suggested by Bill
        Allombert][133X
  
  [33X[0;0YChanged functionality:[133X
  
  [30X    [33X[0;6YIt   is   not   possible   now   to   call  [2XWreathProduct[102X  ([14XReference:
        WreathProduct[114X)  with  2nd  argument  [3XH[103X  not being a permutation group,
        without   using   the   3rd   argument   specifying   the  permutation
        representation.  This is an incompatible change but it will produce an
        error instead of a wrong result. The former behaviour of [2XWreathProduct[102X
        ([14XReference:    WreathProduct[114X)   may   now   be   achieved   by   using
        [2XStandardWreathProduct[102X ([14XReference: StandardWreathProduct[114X) which returns
        the  wreath product for the (right regular) permutation action of [3XH[103X on
        its elements.[133X
  
  [30X    [33X[0;6YThe  function  [10XViewLength[110X  to specify the maximal number of lines that
        are  printed  in  [2XViewObj[102X  ([14XReference: ViewObj[114X) became obsolete, since
        there  was  already  a user preference [10XViewLength[110X to specify this. The
        value of this preference is also accessible in [10XGAPInfo.ViewLength[110X.[133X
  
  
  [1X2.1-2 [33X[0;0YNew and updated packages since [5XGAP[105X[101X[1X 4.6.5[133X[101X
  
  [33X[0;0YAt   the  time  of  the  release  of  [5XGAP[105X  4.6.5  there  were  107  packages
  redistributed  with  [5XGAP[105X.  The  first public release of [5XGAP[105X 4.7 contains 114
  packages.[133X
  
  [33X[0;0YOne  of  essential changes is that the [5XCitrus[105X package by J.Mitchell has been
  renamed  to  [5XSemigroups[105X.  The  package  has  been completely overhauled, the
  performance  has been improved, and the code has been generalized so that in
  the  future  the  same  code  can  be  used  to  compute with other types of
  semigroups.[133X
  
  [33X[0;0YFurthermore,  new  packages that have been added to the redistribution since
  the release of [5XGAP[105X 4.6.5 are:[133X
  
  [30X    [33X[0;6Y[5X4ti2interface[105X  package by Sebastian Gutsche, providing an interface to
        [5X4ti2[105X,  a  software  package for algebraic, geometric and combinatorial
        problems on linear spaces ([7Xhttp://www.4ti2.de[107X).[133X
  
  [30X    [33X[0;6Y[5XCoReLG[105X  by  Heiko  Dietrich,  Paolo  Faccin  and  Willem  de Graaf for
        calculations in real semisimple Lie algebras.[133X
  
  [30X    [33X[0;6Y[5XIntPic[105X  package  by Manuel Delgado, aimed at providing a simple way of
        getting  a  pictorial  view  of sets of integers. The main goal of the
        package  is  producing  [5XTikz[105X  code  for  arrays  of integers. The code
        produced  is  to  be  included  in  a  LaTeX  file,  which can then be
        processed.  Some  of  the  integers  are emphasized by using different
        colors for the cells containing them.[133X
  
  [30X    [33X[0;6Y[5XLieRing[105X  by  Serena  Cicalo  and  Willem  de  Graaf  for  constructing
        finitely-presented    Lie    rings    and   calculating   the   Lazard
        correspondence.  The package also provides a database of small [22Xn[122X-Engel
        Lie rings.[133X
  
  [30X    [33X[0;6Y[5XLiePRing[105X  package by Michael Vaughan-Lee and Bettina Eick, introducing
        a new datastructure for nilpotent Lie rings of prime-power order. This
        allows  to  define  such  Lie rings for specific primes as well as for
        symbolic  primes  and  other  symbolic  parameters.  The  package also
        includes  a  database  of nilpotent Lie rings of order at most [22Xp^7[122X for
        all primes [22Xp > 3[122X.[133X
  
  [30X    [33X[0;6Y[5XModIsom[105X  by Bettina Eick, which contains various methods for computing
        with  nilpotent  associative  algebras.  In  particular, it contains a
        method to determine the automorphism group and to test isomorphisms of
        such  algebras  over  finite  fields  and of modular group algebras of
        finite  [22Xp[122X-groups.  Further, it contains a nilpotent quotient algorithm
        for  finitely presented associative algebras and a method to determine
        Kurosh algebras.[133X
  
  [30X    [33X[0;6Y[5XSLA[105X  by Willem de Graaf for computations with simple Lie algebras. The
        main  topics  of  the  package  are nilpotent orbits, theta-groups and
        semisimple subalgebras.[133X
  
  [33X[0;0YFurthermore,  some  packages  have  been  upgraded  substantially  since the
  [5XGAP[105X 4.6.5 release:[133X
  
  [30X    [33X[0;6Y[5XANUPQ[105X  package  by  Greg  Gamble, Werner Nickel and Eamonn O'Brien has
        been updated after Max Horn joined it as a maintainer. As a result, it
        is now much easier to install and use it with the current [5XGAP[105X release.[133X
  
  [30X    [33X[0;6Y[5XWedderga[105X  package  by  Osnel  Broche  Cristo,  Allen Herman, Alexander
        Konovalov, Aurora Olivieri, Gabriela Olteanu, Ángel del Río and Inneke
        Van  Gelder  has  been  extended  to include functions for calculating
        local  and  global Schur indices of ordinary irreducible characters of
        finite  groups,  cyclotomic  algebras  over abelian number fields, and
        rational quaternion algebras (contribution by Allen Herman).[133X
  
  
  [1X2.2 [33X[0;0Y[5XGAP[105X[101X[1X 4.7.3 (February 2014)[133X[101X
  
  [33X[0;0YFixed bugs which could lead to incorrect results:[133X
  
  [30X    [33X[0;6YIncorrect  result returned by [10XAutomorphismGroup(PSp(4,2^n))[110X. [Reported
        by Anvita][133X
  
  [30X    [33X[0;6YThe  [2XOrder[102X  ([14XReference:  Order[114X)  method  for group homomorphisms newly
        introduced  in  [5XGAP[105X 4.7  had  a bug that caused it to sometimes return
        incorrect results. [Reported by Benjamin Sambale][133X
  
  [33X[0;0YFixed bugs that could lead to break loops:[133X
  
  [30X    [33X[0;6YSeveral bugs were fixed and missing methods were introduced in the new
        code for transformations, partial permutations and semigroups that was
        first  included  in  [5XGAP[105X 4.7.  Some minor corrections were made in the
        documentation for transformations.[133X
  
  [30X    [33X[0;6YBreak  loop  in  [10XIsomorphismFpMonoid[110X when prefixes in generators names
        were  longer  than  one letter. [Reported by Dmytro Savchuk and Yevgen
        Muntyan][133X
  
  [30X    [33X[0;6YBreak      loop      while      displaying      the      result     of
        [2XMagmaWithInversesByMultiplicationTable[102X                     ([14XReference:
        MagmaWithInversesByMultiplicationTable[114X). [Reported by Grahame Erskine][133X
  
  [33X[0;0YImproved functionality:[133X
  
  [30X    [33X[0;6YBetter   detection   of  UTF-8  terminal  encoding  on  some  systems.
        [Suggested by Andries Brouwer][133X
  
  
  [1X2.3 [33X[0;0Y[5XGAP[105X[101X[1X 4.7.4 (February 2014)[133X[101X
  
  [33X[0;0YThis  release  was prepared immediately after [5XGAP[105X 4.7.3 to revert the fix of
  the  error  handling  for  the  single  quote  at  the end of an input line,
  contained  in  [5XGAP[105X  4.7.3. It happened that (only on Windows) the fix caused
  error messages in one of the packages.[133X
  
  
  [1X2.4 [33X[0;0Y[5XGAP[105X[101X[1X 4.7.5 (May 2014)[133X[101X
  
  [33X[0;0YFixed bugs which could lead to incorrect results:[133X
  
  [30X    [33X[0;6Y[2XInstallValue[102X ([14XReference: InstallValue[114X) cannot handle immediate values,
        characters  or booleans for technical reasons. A check for such values
        was  introduced  to  trigger  an  error  message and prevent incorrect
        results caused by this. [Reported by Sebastian Gutsche][133X
  
  [30X    [33X[0;6Y[2XKnowsDictionary[102X   ([14XReference:  KnowsDictionary[114X)  and  [2XLookupDictionary[102X
        ([14XReference:  LookupDictionary[114X) methods for [10XIsListLookupDictionary[110X were
        using  [2XPositionFirstComponent[102X ([14XReference: PositionFirstComponent[114X); the
        latter  is  only  valid on sorted lists, but in [10XIsListLookupDictionary[110X
        the  underlying  list  is  NOT  sorted  in  general,  leading to bogus
        results.[133X
  
  [33X[0;0YOther fixed bugs:[133X
  
  [30X    [33X[0;6YA      bug      in      [10XDirectProductElementsFamily[110X     which     used
        [2XCanEasilyCompareElements[102X ([14XReference: CanEasilyCompareElements[114X) instead
        of [2XCanEasilySortElements[102X ([14XReference: CanEasilySortElements[114X).[133X
  
  [30X    [33X[0;6YFixed  wrong  [10XInfolevel[110X  message  that  caused  a  break loop for some
        automorphism group computations.[133X
  
  [30X    [33X[0;6YFixed  an  error  that  sometimes  caused a break loop in [2XHallSubgroup[102X
        ([14XReference: HallSubgroup[114X). [Reported by Benjamin Sambale][133X
  
  [30X    [33X[0;6YFixed  a  rare  error  in computation of conjugacy classes of a finite
        group   by   homomorphic  images,  providing  fallback  to  a  default
        algorithm.[133X
  
  [30X    [33X[0;6YFixed  an error in the calculation of Frattini subgroup in the case of
        the trivial radical.[133X
  
  [30X    [33X[0;6YSeveral  minor  bugs  were  fixed  in  the  documentation, kernel, and
        library code for transformations.[133X
  
  [30X    [33X[0;6YFixed  errors  in [2XNumberPerfectGroups[102X ([14XReference: NumberPerfectGroups[114X)
        and [2XNumberPerfectLibraryGroups[102X ([14XReference: NumberPerfectLibraryGroups[114X)
        not being aware that there are no perfect groups of odd order.[133X
  
  [30X    [33X[0;6YRestored  the  ability  to  build  [5XGAP[105X on OS X 10.4 and 10.5 which was
        accidentally  broken  in  the  previous [5XGAP[105X release by using the build
        option not supported by these versions.[133X
  
  [30X    [33X[0;6YFixed  some  problems  for  ia64 and sparc architectures. [Reported by
        Bill Allombert and Volker Braun][133X
  
  [33X[0;0YNew package added for the redistribution with [5XGAP[105X:[133X
  
  [30X    [33X[0;6Y[5Xpermut[105X   package   by   A.Ballester-Bolinches,   E.Cosme-Llópez,   and
        R.Esteban-Romero to deal with permutability in finite groups.[133X
  
  
  [1X2.5 [33X[0;0Y[5XGAP[105X[101X[1X 4.7.6 (November 2014)[133X[101X
  
  [33X[0;0YFixed bugs which could lead to incorrect results:[133X
  
  [30X    [33X[0;6YA  bug  that may cause [2XShortestVectors[102X ([14XReference: ShortestVectors[114X) to
        return an incomplete list. [Reported by Florian Beye][133X
  
  [30X    [33X[0;6YA  bug  that may lead to incorrect results and infinite loops when [5XGAP[105X
        is compiled without GMP support using gcc 4.9.[133X
  
  [30X    [33X[0;6YA    bug    that    may    cause    [2XOrthogonalEmbeddings[102X   ([14XReference:
        OrthogonalEmbeddings[114X)  to  return  an  incomplete result. [Reported by
        Benjamin Sambale][133X
  
  [33X[0;0YFixed bugs that could lead to break loops:[133X
  
  [30X    [33X[0;6Y[2XClosureGroup[102X  ([14XReference:  ClosureGroup[114X)  should  be  used  instead of
        [2XClosureSubgroup[102X  ([14XReference:  ClosureSubgroup[114X)  in  case  there  is no
        parent group, otherwise some calculations such as e.g. [2XNormalSubgroups[102X
        ([14XReference: NormalSubgroups[114X) may fail. [Reported by Dmitrii Pasechnik][133X
  
  [30X    [33X[0;6YFixed  a line in the code that used a hard-coded identity permutation,
        not a generic identity element of a group. [Reported by Toshio Sumi][133X
  
  [30X    [33X[0;6YFixed a problem in the new code for calculating maximal subgroups that
        caused  a  break  loop  for  some  groups  from  the transitive groups
        library. [Reported by Petr Savicky][133X
  
  [30X    [33X[0;6YFixed  a  problem  in [2XClosureSubgroup[102X ([14XReference: ClosureSubgroup[114X) not
        accepting some groups without [2XParent[102X ([14XReference: Parent[114X). [Reported by
        Inneke van Gelder][133X
  
  [33X[0;0YOther fixed bugs:[133X
  
  [30X    [33X[0;6YEliminated  a  number  of  compiler  warnings detected with some newer
        versions of [5XC[105X compilers.[133X
  
  [30X    [33X[0;6YSome minor bugs in the transformation and partial permutation code and
        documentation were resolved.[133X
  
  
  [1X2.6 [33X[0;0Y[5XGAP[105X[101X[1X 4.7.7 (February 2015)[133X[101X
  
  [33X[0;0YNew features:[133X
  
  [30X    [33X[0;6YIntroduced  some  arithmetic  operations  for  infinity  and  negative
        infinity, see [14XReference: infinity[114X.[133X
  
  [30X    [33X[0;6YIntroduced    new    property    [2XIsGeneratorsOfSemigroup[102X   ([14XReference:
        IsGeneratorsOfSemigroup[114X)  which reflects wheter the list or collection
        generates a semigroup.[133X
  
  [33X[0;0YFixed bugs which could lead to incorrect results:[133X
  
  [30X    [33X[0;6YFixed  a  bug  in  [2XUnion[102X ([14XReference: Union[114X) (actually, in the internal
        library  function  [10XJoinRanges[110X)  caused  by  downward  running  ranges.
        [Reported by Matt Fayers][133X
  
  [30X    [33X[0;6YFixed  a  bug  where recursive records might be printed with the wrong
        component  name, coming from component names being ordered differently
        in two different pieces of code. [Reported by Thomas Breuer][133X
  
  [30X    [33X[0;6YThe  usage  of [10Xabs[110X in [11Xsrc/gmpints.c[111X was replaced by [10XAbsInt[110X. The former
        is  defined  to  operate on 32-bit integers even if [5XGAP[105X is compiled in
        64-bit  mode.  That lead to truncating [5XGAP[105X integers and caused a crash
        in  [2XRemInt[102X  ([14XReference: RemInt[114X), reported by Willem De Graaf and Heiko
        Dietrich.  Using  [10XAbsInt[110X  fixes  the  crash,  and  ensures the correct
        behaviour on 32-bit and 64-bit builds.[133X
  
  [33X[0;0YFixed bugs that could lead to break loops:[133X
  
  [30X    [33X[0;6YA  problem  with  [2XProbabilityShapes[102X ([14XReference: ProbabilityShapes[114X) not
        setting  frequencies  list  for  small  degrees.  [Reported  by Daniel
        Błażewicz and independently by Mathieu Gagne][133X
  
  [30X    [33X[0;6YAn  error when generating a free monoid of rank infinity. [Reported by
        Nick Loughlin][133X
  
  [30X    [33X[0;6YSeveral  bugs  with  the  code for Rees matrix semigroups not handling
        trivial cases properly.[133X
  
  [30X    [33X[0;6YA     bug    in    [2XIsomorphismTypeInfoFiniteSimpleGroup[102X    ([14XReference:
        IsomorphismTypeInfoFiniteSimpleGroup[114X)  affecting  one particular group
        due  to  a  misformatting  in  a  routine  that translates between the
        Chevalley  type  and the name used in the table (in this case, [10X"T"[110X was
        used instead of [10X["T"][110X). [Reported by Petr Savicky][133X
  
  [33X[0;0YOther fixed bugs:[133X
  
  [30X    [33X[0;6YThe  [2XBasis[102X  ([14XReference:  Basis[114X) method for full homomorphism spaces of
        linear  mappings  did not set basis vectors which could be obtained by
        [2XGeneratorsOfLeftModule[102X ([14XReference: GeneratorsOfLeftModule[114X).[133X
  
  [30X    [33X[0;6YA problem with [2XGaloisType[102X ([14XReference: GaloisType[114X) entering an infinite
        loop  in  the  routine  for  approximating a root. [Reported by Daniel
        Błażewicz][133X
  
  [30X    [33X[0;6YFixed the crash when [5XGAP[105X is called when the environment variables [10XHOME[110X
        or [10XPATH[110X are unset. [Reported by Bill Allombert][133X
  
  [33X[0;0YFurthermore,  new  packages that have been added to the redistribution since
  the release of [5XGAP[105X 4.7.6 are:[133X
  
  [30X    [33X[0;6Y[5Xjson[105X package by Christopher Jefferson, providing a mapping between the
        [5XJSON[105X markup language and [5XGAP[105X[133X
  
  [30X    [33X[0;6Y[5XSglPPow[105X package by Bettina Eick and Michael Vaughan-Lee, providing the
        database of [22Xp[122X-groups of order [22Xp^7[122X for [22Xp > 11[122X, and of order [22X3^8[122X.[133X
  
  
  [1X2.7 [33X[0;0Y[5XGAP[105X[101X[1X 4.7.8 (June 2015)[133X[101X
  
  [33X[0;0YFixed bugs which could lead to incorrect results:[133X
  
  [30X    [33X[0;6YAdded  two  groups of degree 1575 which were missing in the library of
        first primitive groups. [Reported by Gordon Royle][133X
  
  [30X    [33X[0;6YFixed  the  error  in  the  code for algebra module elements in packed
        representation  caused  by the use of [2XObjectify[102X ([14XReference: Objectify[114X)
        with  the  type of the given object instead of [2XObjByExtRep[102X ([14XReference:
        ObjByExtRep[114X)  as  recommended  in  [14X'Reference: Further Improvements in
        Implementing   Residue  Class  Rings'[114X.  The  problem  was  that  after
        calculating  [10Xu+v[110X  where one of the summands was known to be zero, this
        knowledge  was  wrongly  passed  to the sum via the type. [Reported by
        Istvan Szollosi][133X
  
  [30X    [33X[0;6YFixed  a  bug  in [2XPowerMod[102X ([14XReference: PowerMod[114X) causing wrong results
        for  univariate  Laurent polynomials when the two polynomial arguments
        are stored with the same non-zero shift. [Reported by Max Horn][133X
  
  [33X[0;0YFurthermore,  new  packages that have been added to the redistribution since
  the release of [5XGAP[105X 4.7.7 are:[133X
  
  [30X    [33X[0;6Y[5XPatternClass[105X  by  Michael  Albert,  Ruth  Hoffmann  and  Steve Linton,
        allowing  to  explore  the  permutation pattern classes build by token
        passing  networks. Amongst other things, it can compute the basis of a
        permutation pattern class, create automata from token passing networks
        and  check if the deterministic automaton is a possible representative
        of a token passing network.[133X
  
  [30X    [33X[0;6Y[5XQPA[105X  by Edward Green and Øyvind Solberg, providing data structures and
        algorithms  for computations with finite dimensional quotients of path
        algebras,  and  with finitely generated modules over such algebras. It
        implements  data  structures  for quivers, quotients of path algebras,
        and  modules, homomorphisms and complexes of modules over quotients of
        path algebras.[133X
  
  
  [1X2.8 [33X[0;0Y[5XGAP[105X[101X[1X 4.7.9 (November 2015)[133X[101X
  
  [33X[0;0YFixed bug which could lead to incorrect results:[133X
  
  [30X    [33X[0;6YFixed  an error in [10XDataAboutSimpleGroup[110Xcalculation, which caused wrong
        result  in  calculation of the automorphism group of [22XJ_2[122X. [Reported by
        Fatemeh Koorepazan-Moftakhar][133X
  
  [33X[0;0YImproved and extended functionality:[133X
  
  [30X    [33X[0;6Y[2XGModuleByMats[102X  ([14XReference:  GModuleByMats[114X)  and some related functions
        now  work  for  infinite  fields,  in  particular in characteristic 0.
        However, this only applies for functions that do not need the MeatAxe,
        as that is still tied to finite fields.[133X
  
