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1. Introduction

### 1. Introduction

Groupoids are mathematical categories in which every arrow is invertible. The Gpd 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 [Moo01] 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 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 2.010 for GAP 4.4 - Murat Alp and Chris Wensley
    ------------------------------------------------------------
    -----------------------------------------------------------
    loading Gpd 1.03 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: GroupoidMorphismWithCommonRange
    [8] Gpd: GroupoidMorphism
    [9] Gpd: GroupoidMorphismByComponents
    [10] Gpd: GroupoidMorphismByUnion
    [11] Gpd: GroupoidsOfGraphOfGroupoids

Once the package is loaded, it is possible to check the correct installation by running the test suite of the package with the following command. (The test file itself is `tst/gpd_manual.tst`.)

    gap> ReadPackage( "gpd", "tst/testall.g" );
    + Testing all example commands in the Gpd manual
    + GAP4stones: 0
    true

You may reference this package by mentioning [BMPW02] and [Moo01].

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