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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.

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 Gpd 1.05 for GAP 4.4 - Emma Moore and Chris Wensley
    -----------------------------------------------------------
    true

For version 1.05 the package has been completely restructured, starting with magmas with objects and their mappings, and building up to groupoids via semigroups with objects and monoids with objects. This development is ongoing, and this manual does not mention all the available functions. A new version will be released as soon as possible.

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 examples in Chapter 2 of the Gpd manual
    + GAP4stones: 1250
    + Testing examples in Chapter 3 of the Gpd manual
    + GAP4stones: infinity
    + Testing examples in Chapter 4 of the Gpd manual
    + GAP4stones: 416
    + Testing examples in Chapter 5 of the Gpd manual
    + GAP4stones: 2500
    + Testing examples in Chapter 6 of the Gpd manual
    + GAP4stones: 28

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

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