Homepage van Jan De Beule



GAP is a famous system for computational discrete algebra. Its group theoretical and algebraic capabilities, together with a very good documentation and a design to encourage users to write software packages extending GAP itself, make it the perfect environment to develop software to study finite geometry and related topics. My research of the past years and my interest for computational mathematics lead to some GAP-packges: PG, Forms and FinInG.


Forms, a package for sesquilinear and quadratic forms is a package, developed by John Bamberg and Jan De Beule. It can be used for work with sesquilinear and quadratic forms, objects that are used to describe polar spaces and classical groups. The package also deals with the recognition of certain matrix groups preserving a sesquilinear or quadratic form. The main features of forms are its facility with creating sesquilinear and quadratic forms via matrices and polynomials, and in changing forms (creation of isometries). This GAP package is accepted since 2009. It is distributed together with GAP. Its latest version is also available at the Forms website.


FinInG is a GAP package for computation in Finite Incidence Geometry developed by John Bamberg, Anton Betten, Philippe Cara, Jan De Beule, Michel Lavrauw and Max Neunhoeffer. The package provides basic tools to work in various areas of finite geometry from the realms of projective spaces to the flat lands of generalised polygons. FinInG relies on the algebraic power of GAP and some of its packages, in particular on the functionality with matrix and permutation groups.

The package is accepted since 2018, and distributed together with GAP. More information and its latest version can be found at the official FinInG website


In January 2016, I started contributing to GAP package digraphs, which is a new package for (directed) graphs and (directed) multigraphs. This package also provides an interface to bliss (a tool for computing automorphism groups and canonical labelings of graphs), by Tommi Junttila and Petteri Kaski.


PG, a share package for GAP as well, stands for Projective Geometries. This package is de predecessor of FinInG. The development of the package was done in two master thesis projects under supervision of Leo Storme. The development was started by Patrick Govaerts and was continued by Jan De Beule. Further contributions were done by Peter Lemens and Anja Hallez. However, since 2006 the development of FinInG was initiated, and PG remained unchanged. It can still be found at the undeposited esection of the GAP website. The last stable version for GAP4r4 can be downloaded here, the manuel can be read here. Top

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