GAP (Gpd) - Chapter 5: Development History

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### 5. Development History

#### 5.1 Versions of the Package

The first version, GraphGpd 1.001, formed part of Emma Moore's thesis [M01] in December 2000, but was not made generally available.

Version 1.002 of GraphGpd was prepared to run under GAP 4.4 in January 2004; was submitted to the GAP council to be considered as an accepted package; but suggestions from the referee were not followed up.

In April 2006 the manual was converted to GAPDoc format. Variables `Star`, `Costar` and `CoveringGroup` were found to conflict with usage in other packages, and were renamed `VertexStar`, `VertexCostar` and `CoveringGroupOfGroupoid` respectively. Similarly, the `Vertices` and `Arcs` of an `FpWeightedDigraph` were changed from attributes to record components.

In the spring of 2006 the package was extensively rewritten and renamed Gpd. Version 1.01 was submitted as a deposited package in June 2006.

#### 5.2 What needs to be done next?

Computationally, there are three types of connected groupoid:

- those with identical object groups,

- those with object groups conjugate in some supergroup,

- those with object groups which are simply isomorphic.

GraphGpd attempted to implement the second case. Gpd 1.01 restricts itself to the first case. Gpd 1.02 will extend 1.01 to the second case.

Here are some other immediate requirements:

- normal subgroupoids and quotient groupoids;

- more methods for morphisms of groupoids, particularly when the range is not connected;

- `ImageElm` and `ImagesSource` for the cases of groupoid morphisms not yet covered;

- `Enumerator` for `IsHomsetCosetsRep`;

- free groupoid on a graph;

- methods for `FreeProductWithAmalgamation` and `HnnEntension` for pc-groups;

- convert `GraphOfGroupsRewritingSystem` to the category `IsRewritingSystem`;

- in XMod, implement crossed modules over groupoids.

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