Several computer programs, written as part of
EPSRC grant GR/S75581/01,
are found below. These form a suite of tools for
investigating Abelian and quadratic differentials, built in
specified ways from rectangular pieces, on Riemann surfaces
and their nonorientable equivalents. You can download the
source code for these programs below.
- Part calculates Rauzy classes of permutations and finds loops in them whose associate Rauzy cocycle is primitive irreducible (this is Veech's construction of pseudo-Anosov homeomorphisms with orientable invariant foliations). It draws pictures of the Markov partitions, works out the Markov transition matrix and substitution, works out the characteristic polynomial of the transition matrix, and draws images of two-dimensional slices of the Franks-Fathi semiconjugacy. All this information is presented on generated webpages; see examples here and here. To get Part, first see the installation instructions, and then download either the Windows executable. To run the latter you will need ImageMagick installed.
- Pit performs an algorithm which looks for coincidences in translation surfaces coming from a given Rauzy class. To compile Pit, you first need GamutCore and Modular. Please note: the build system for Pit is undergoing surgery and may not yet work as expected.
- Gamut contains code which deals with quadratic differentials. It can help to investigate (for example) the Burau representation of the braid group. To compile Gamut you first need Modular and GamutCore and GamutBase and Modular, built in that order. Please note: the build system for Gamut is undergoing surgery and may not yet work as expected.