11 Development history
  
  This  chapter, which contains details of the major changes to the package as
  it  develops,  was  first created in April 2002. Details of the changes from
  XMod  1 to XMod 2.001 are far from complete. Starting with version 2.009 the
  file CHANGES lists the minor changes as well as the more fundamental ones.
  
  The  inspiration  for  this  package  was  the  need,  in the mid-1990's, to
  calculate  induced  crossed  modules  (see  [BW95], [BW96], [BW03]). GAP was
  chosen  over  other  computational group theory systems because the code was
  freely  available,  and  it was possible to modify the Tietze transformation
  code so as to record the images of the original generators of a presentation
  as  words  in  the  simplified  presentation. (These modifications are now a
  standard part of the Tietze transformation package in GAP.)
  
  
  11.1 Changes from version to version
  
  
  11.1-1 Version 1 for GAP 3
  
  The  first  version  of  XMod  became  an  accepted package for GAP 3.4.3 in
  December 1996.
  
  
  11.1-2 Version 2
  
  Conversion  of  XMod 1 from GAP 3.4.3 to the new GAP syntax began soon after
  GAP  4  was  released,  and  had  a  lengthy  gestation.  The new GAP syntax
  encouraged  a re-naming of many of the function names. An early decision was
  to  introduce  generic  categories  2dDomain  for  (pre-)crossed modules and
  (pre-)cat1-groups, and 2dMapping for the various types of morphism. In 2.009
  3dDomain  was  used  for  crossed squares and cat2-groups, and 3dMapping for
  their  morphisms.  A  generic  name  for  derivations  and  sections is also
  required, and Up2dMapping is currently used.
  
  
  11.1-3 Version 2.001 for GAP 4
  
  This  was  the  first  version of XMod for GAP 4, completed in April 2002 in
  time  for  the  release of GAP 4.3. Functions for actors and induced crossed
  modules  were  not  included,  nor many of the functions for derivations and
  sections, for example InnerDerivation.
  
  
  11.1-4 Induced crossed modules
  
  During  May  2002  converted  the code for induced crossed modules. (Induced
  cat1-groups may be converted one day.)
  
  
  11.1-5 Versions 2.002 -- 2.006
  
  Version  2.004  of  April  14th  2004  added the Cat1Select functionality of
  version 1 to the Cat1 function.
  
  A  significant  addition  in  Version  2.005 was the conversion of the actor
  crossed   module   functions   from   the   3.4.4   version.  This  included
  AutomorphismPermGroup  for  a  crossed  module,  WhiteheadXMod,  NorrieXMod,
  LueXMod,   ActorXMod,   Centre   of  a  crossed  module,  InnerMorphism  and
  InnerActorXMod.
  
  
  11.1-6 Versions 2.007 -- 2.010
  
  These versions contain changes made between September 2004 and October 2007.
  
      Added  basic  functions  for  crossed squares, considered as 3dObjects
        with  crossed  pairings,  and  their morphisms. Groups with two normal
        subgroups,  and  the  actor  of  a  crossed  module,  provide standard
        examples of crossed squares. (Cat2-groups are not yet implemented.)
  
      Converted the documentation to the format of the GAPDoc package.
  
      Improved  AutomorphismPermGroup  for crossed modules, and introduced a
        special method for conjugation crossed modules.
  
      Substantial   revisons  made  to  XModByCentralExtension,  NorrieXMod,
        LueXMod, ActorXMod, and InclusionInducedXModByCopower.
  
      Version 2.010, of October 2007, was timed to coincide with the release
        of  GAP  4.4.10,  and included a change of filenames; and correct file
        protection codes.
  
  
  11.2 Versions for GAP [4.5 .. 4.8]
  
  Version 2.19, released on 9th June 2012, included the following changes:
  
      The  file  makedocrel.g  was  copied,  with  appropriate changes, from
        GAPDoc, and now provides the correct way to update the documentation.
  
      The first functions for crossed modules of groupoids were introduced.
  
      A GNU General Public License declaration was added.
  
  
  11.2-1 AllCat1s
  
  Version  2.21  contained major changes to the Cat1Select operation: the list
  CAT1_LIST  of  cat1-structures  in the data file cat1data.g was changed from
  permutation groups to pc-groups, with the generators of subgroups; images of
  the tail map; and images of the head map being given as ExtRepOfObj of words
  in the generators.
  
  The AllCat1s function was reintroduced from the GAP3 version, and renamed as
  the operation AllCat1sBasic.
  
  In  version  2.25 the data in cat1data.g was extended from groups of size up
  to  48  to groups of size up to 70. In particular, the 267 groups of size 64
  give  rise  to  a total of 1275 cat1-groups. The authors are indebted to Van
  Luyen  Le  in  Galway  for pointing out a number of errors in the version of
  this list distributed with version 2.24 of this package.
  
  
  11.2-2 Versions 2.43 - 2.56
  
  Version  2.43,  released  on  11th  November  2015,  included  the following
  changes:
  
      The material on isoclinism in Chapter 4 was added.
  
      The         package         webpage         has        moved        to
        http://pages.bangor.ac.uk/~mas023/chda/.
  
      A        GitHub        repository        was        started        at:
        https://github.com/gap-packages/xmod.
  
      The  section  on  Distinct and Common Representatives was moved to the
        Utils package.
  
  
  11.2-3 Version 2.61
  
  Major  changes  in names took place, with 2dDomain, 2dGroup, 2dMapping, etc.
  becoming  2DimensionalDomain,  2DimensionalGroup, 2DimensionalMapping, etc.,
  and  similarly  for 3-dimensional versions. Also HigherDimensionalDomain and
  related  categories,  domains,  properties,  attributes  and operations were
  introduced.  At  the same time, functions for cat2-groups were introduced by
  Alper Odabas.
  
  
  11.2-4 Latest Version
  
  The latest version, 2.64, was released on 30th November 2017.
  
  
  11.3 What needs doing next?
  
      Speed up the calculation of Whitehead groups.
  
      Add more functions for 3dObjects and implement cat2-groups.
  
      Improve  interaction with the package groupoids implementing the group
        groupoid  version  of  a crossed module, and adding more functions for
        crossed modules of groupoids.
  
      Add interaction with IdRel (and possibly XRes and natp) .
  
      Need   InverseGeneralMapping  for  morphisms  and  more  features  for
        FpXMods, PcXMods, etc.
  
      Implement actions of a crossed module.
  
      Implement FreeXMods and an operation Isomorphism2dDomains.
  
      Allow the construction of a group of morphisms of crossed modules.
  
      Complete  the conversion from Version 1 of the calculation of sections
        using EndoClasses.
  
      More crossed square constructions:
  
            If  M,  N  are  ordinary P-modules and A is an arbitrary abelian
              group  on which P acts trivially, then there is a crossed square
              with sides
  
  
              0  : A \to N,\quad 0 : A \to M,\quad 0 : M \to P,\quad 0 : N \to
              P.
  
  
  
            For a group L, the automorphism crossed module Act L = (ι : L ->
              Aut  L) splits to form the square with (ι_1 : L -> Inn L) on two
              sides,  and (ι_2 : Inn L -> Aut L) on the other two sides, where
              ι_1  maps  l  ∈  L to the inner automorphism β_l : L -> L, l^' ↦
              l^-1l^'l,  and  ι_2  is  the  inclusion  of  Inn L in Aut L. The
              actions are standard, and the crossed pairing is
  
  
              \boxtimes  \;:\;  {\rm  Inn}\ L \times {\rm Inn}\ L \to L, \quad
              (\beta_l, \beta_{l^{\prime}}) \;\mapsto\; [l, l^{\prime}]~.
  
  
  
      Improve the interaction with the HAP package.