This package provides a collection of methods for working with arrangements. These methods are capable of computing many topological and combinatorial objects associated to an arrangement. Computed data is cached within the arrangement object.
When there is more than one method of computing a particular invariant, then the package will try to find the most efficient means. It will take into consideration both previously computed information as well as computation time for new data.
I have used this package along with a table of linear spaces constructed by Anton Betten and Dieter Betten ("Linear spaces with at most 12 points" Journal of Combinatorial Designs 7 (1999), 119--145) to construct a partial database of hyperplane arrangements with up to 10 lines. Since I have changed interests from research mathematics to computer security I am posting this database on this site in hopes that it may be of some use.
The database is an SQLite 3 database with a single table,
arrdb. I can make no promises about the correctness of
this table. I can say for certain that I had an error in my algorithm
for determining the number of connected components of the realization
space. Therefore, RS_NrConnectedComponents consists entirely of NULL
values. My (occasionally incorrect) counts are preserved in the
RS_IncorrectNrConnectedComponents column.
The code used to compute the realization spaces is located in the matroid.gi file in my arrangement package (which probably needs modified to work in current versions of GAP; the last known compatible version was GAP 4.4.9). The matroid file is fairly well commented though, so should be an easy read.
SQLite 3 Arrangement database and schema
Download GAP from the GAP download page. (You will need the "gap4" archive as well as the "packages" archive) Note for Mac OS X users: You will need to install the apple developer tools (free registration required) and I recommend installing Fink (in particular, the "gmp" and "gmp-shlibs" packages).
To install this package, download and extract it (it will create an "arrangement" folder). Drag this folder to the "pkg" folder in your GAP directory. You will also need to do this with Frank Lübeck's FUtil.
LoadPackage("Arrangement");
Here's the GAP Manual, as well as a One page reference.