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9. Development history
9.1 Changes from version to version
9.1-1 Version 1 for GAP 3
9.1-2 Version 2
9.1-3 Version 2.001 for GAP 4
9.1-4 Induced crossed modules
9.1-5 Versions 2.002 -- 2.006
9.1-6 Versions 2.007 -- 2.008
9.1-7 Version 2.010
9.2 What needs doing next?

### 9. 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.)

#### 9.1 Changes from version to version

##### 9.1-1 Version 1 for GAP 3

The first version of XMod became an accepted package for GAP 3.4.3 in December 1996.

##### 9.1-2 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 names `2dObject` for (pre-)crossed modules and (pre-)cat1-groups, and `2dMapping` for the various types of morphism. In 2.009 `3dObject` is 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.

##### 9.1-3 Version 2.001 for GAP 4

This was the first version of XMod for GAP 4, completed in April 2002 in a rush to catch 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`.

##### 9.1-4 Induced crossed modules

During the period May 20th - May 27th 2002 converted `induce.g` to `induce.gd` and `induce.gi` (later renamed `induce2.gd`, `induce2.gi`), at least as regards induced crossed modules. (Induced cat1-groups may be convereted one day.) For details, see the file `CHANGES`.

##### 9.1-5 Versions 2.002 -- 2.006

Version 2.002 was prepared for the 4.4 release at the end of January 2004.

Version 2.003 of February 28th 2004 just fixed some file protections.

Version 2.004 of April 14th 2004 added the `Cat1Select` functionality of version 1 to the `Cat1` function (see also version 2.007).

Version 2.005 of April 16th 2004 moved the example files from `tst/test_i.g` to `examples/example_i.g`, and converted `testmanual.g` to a proper test file `tst/xmod_manual.tst`.

A significant change was the conversion of the actor crossed module functions from the `3.4.4` version, including `AutomorphismPermGroup` for a crossed module, `WhiteheadXMod`, `NorrieXMod`, `LueXMod`, `ActorXMod`, `Centre` of a crossed module, `InnerMorphism` and `InnerActorXMod`.

##### 9.1-6 Versions 2.007 -- 2.008

These versions contain changes made between September 2004 and October 2006.

- 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`.

- Reintroduced the `Cat1Select` operation.

##### 9.1-7 Version 2.010

The latest version, of October 2007, timed to coincide with the release of GAP 4.4.10, includes a change of filenames; correct file protection codes; and an improvement to `AutomorphismPermGroup` for crossed modules.

#### 9.2 What needs doing next?

- Speed up the calculation of Whitehead groups.

- Add more functions for `3dObjects` and implement `cat2-groups`.

- Add interaction with package Gpd implementing group groupoid version of a crossed module and crossed modules over groupoids.

- Add interaction with IdRel, XRes, and natp.

- Need `InverseGeneralMapping` for morphisms.

- Need more features for `FpXMods`, `PcXMods`, etc.

- Implement actions of a crossed module.

- Implement `FreeXMods`.

- Implement an operation `Isomorphism2dObjects`.

- Allow the construction of a group of morphisms of crossed modules.

- Complete the conversion from Version 1 of the calculation of sections using `EndoClasses`.

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