Short Description of PG

pg, Projective Geometries is a share package for GAP 4, the well known CAS. pg is developed mainly with GAP 4 release 1. It works without any problems under GAP4 release 2. Its aim is to set up an environment for doing finite projective geometry in GAP. Researchers who want to look for examples or counterexamples should be able to setup the environment of the problem without a lot of programming. Therefore general functions are provided in pg, such as calling projective spaces, functions dealing with subspaces, collineations and the collineation group and quadrics and hermtian varieties. Because many functions in GAP deal with permutation groups, we added functions that convert the collineation group into a permutation group.  For more information, you can check the manual of pg.

History, download and technical information

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.  The package remained unchangend since July 2000. Since October 2004, Peter Lemens, a master thesis student works on the further development. Peter has worked/still works on the implementation of polarities, a better implementation to compute te action of the collineationgroup on the points, and the implementation of Grasmann coordinates. From October 2005, a new master thesis student, Anja Hallez, also continued the development. She implemented subgeometries and new functions for quadrics and Hermtitian varieties. In the meantime, pg was submitted to the GAP-group in November 2004. Based on the reports of John Bamberg and Maska Law, we decided to implement again the core of the pg package so that it integrates better with the existing functionality of GAP. This project has already been started by John Bamberg, Maska Law and Max Neunhoffer and will continue from september 2006.

The version of 2000 can be downloaded here. As the package was mainly developped using GAP4r1, and mainly used with GAP4r2 and GAP4r3, and since there was a slight change in the package loading system, we provide a version for GAP4r3 and GAP4r4.

You can download pg here.

GAP4r3 GAP4r4
tgz tgz

You are of course permitted to share the package with colleagues, but you are not permitted to distribute modified versions. If you have comments, suggestions or if you find bugs, please contact Jan De Beule. You can install the package as a standard gap share package: copy the file into your local pkg directory and unpack pg.zoo with unzoo. Afterwards, you can start gap (possible with the -l option to set the path) and load the package with the command RequirePackage("pg") (GAP4r3) or, LoadPackage("pg") (GAP4r4) . If you have problems or questions read the manual or, if everything fails, contact Jan De Beule.

It is possible that font problems occur when viewing the manual under X. To solve the problems, try the following steps:

(1) Add the following line to the file .Xdefaults (or .Xresources):

Netscape*documentFonts.charset*adobe-fontspecific:   iso-8859-1
(2) Issue the following command or restart the X server:
xrdb .Xdefaults
(3) Restart netscape

The adjustments are related with some configurations about fonts. More information about the problem is available here

Successor of PG

Currently, pg is not further developed. The part of PG dealing with sesquilinear and quadratic forms was further developed (together with John Bamberg) and resulted in the official GAP-package forms. The more geometric functionality of pg was moved to and further developed in the GAP package FinInG in cooperation with many other people, in the GAP package FinInG. See the official FinInG page.
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