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GAP 4 Package FinInG

Finite Incidence Geometry

1.3

2015

John Bamberg, Anton Betten, Philippe Cara, Jan De Beule, Michel Lavrauw, Max Neunhoeffer.

Copyright

© 2015 by the authors

This package may be distributed under the terms and conditions of the GNU Public License Version 2 or higher.

The development group of FinInG welcomes contact with users. In case you have obtained the package as a deposited package part of archive during the installation of GAP, we call on your beneficence to register at http://cage.ugent.be/fining when you use FinInG.

Please tell us about the use of FinInG in your research or teaching. We are very interested in results obtained using FinInG and we might refer to your work in the future. If your work is published, we ask you to cite FinInG like a journal article or book. We provide the necessary BibTex and LaTeX code in Section 1.2.

Acknowledgements

The development phase of FinInG started roughly in 2005. The idea to write a package for projective geometry in GAP had emerged before, and resulted in pg, a relic that still can be found in the undeposited packages section of the GAP website. One of the main objectives was to develop the new package was to create a tighter connection between finite geometry and the group theoretical functions present in GAP.

The authors thank Michael Pauley, Maska Law and Sven Reichard, for their contributions during the early days of the project.

Jan De Beule and Michel Lavrauw have been supported by the Research Foundation Flanders -- Belgium (FWO), and John Bamberg has been supported by a Marie Curie grant and an ARC grant during almost the whole development phase of FinInG. The authors are grateful for this support.

John Bamberg, Philippe Cara and Jan De Beule have spent several weeks in Vicenza while developing FinInG. We acknowledge the hospitality of Michel Lavrauw and Corrado Zanella. Our stays in Vicenza were always fruitful and very enjoyable. During or daily morning and afternoon coffee breaks, we discussed several topics, while enjoying coffee in Caffe Pigaffeta, http://www.caffepigafetta.it. Although one cannot acknowledge everybody, such as the bakery who provided us with the sandwiches, we acknowledge very much the hospitality of Carla and Luigi, who introduced us to many different kinds of coffees from all over the world.

Contents

1 Introduction
2 Examples
3 Incidence Geometry
4 Projective Spaces
5 Projective Groups
6 Polarities of Projective Spaces
7 Finite Classical Polar Spaces
8 Orbits, stabilisers and actions
9 Affine Spaces
10 Geometry Morphisms
11 Algebraic Varieties
12 Generalised Polygons
13 Coset Geometries and Diagrams
A The structure of FinInG
B The finite classical groups in FinInG
C Low level functions for morphisms
References
Index

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