1. Introduction

Groupoids are mathematical categories in which every arrow is invertible. The Gpd share package provides functions for the computation with groupoids and their morphisms; for graphs of groups and graphs of groupoids. The package is far from complete, and development continues.

It was used by Emma Moore in her thesis [M01] to calculate normal forms for Free Products with Amalgamation, and for HNN-extensions, when the initial groups have rewrite systems.

Gpd is implemented using {\GAP}~4.4. Some of the utility functions in the XMod share package for crossed modules are used.

The information parameter InfoGpd takes default value 1 which, for the benefit of new users, causes more messages to be printed out when operations fail. When raised to a higher value, additional information is printed out.

Help is available in the usual way.



gap> LoadPackage( "gpd" );
------------------------------------------------------------
loading XMod 2.007 for GAP 4.4 - Murat Alp and Chris Wensley
------------------------------------------------------------
-----------------------------------------------------------
loading Gpd 1.01 for GAP 4.4 - Emma Moore and Chris Wensley
-----------------------------------------------------------
true
gap> ?Groupoid
Help: several entries match this topic - type ?2 to get match [2]

[1] Gpd: Groupoid
[2] loops (not loaded): groupoid
[3] Gpd: Groupoids
[4] Gpd: Groupoids: their elements and attributes
[5] Gpd: GroupoidByUnion
[6] Gpd: GroupoidElement
[7] Gpd: GroupoidMorphismByComponents
[8] Gpd: GroupoidMorphism
[9] Gpd: GroupoidsOfGraphOfGroupoids


You may reference this package by mentioning [BM+02] and [M01].




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