Software for lattice triangle groups
The goal of this page is to distribute software that performs the verifications needed in my work with Julien Paupert and John Parker, see "New non-arithmetic complex hyperbolic lattices" part 1 and part 2.
Download spocheck HERE.
If you have run a standard installation of giac, you may be able to simply use "make" in the main directory (it may require changing some options in the Makefile). More information can be found in the README file.
In order to run the program, you will need a recent version of
giac. I suggest using version
1.5.0-81. Alternatively, you could try the latest version, see
but I don't promise any backwards compatibility...
You may also need to install some of the dependencies needed to
compile giac from source, for Ubuntu you should be able to type the
Feel free to let me know if you need help installing spocheck, I would appreciate feedback.
If you manage to compile the program, it will
The program will perform exact computations whenever possible, and use interval arithmetic in order to determine the sign of some numbers (when finished, the program will tell you how many digits it had to use in order to check all needed signs).
The program is written in C++ and uses Bernard Parisse's giac libraries. My main motivation for using giac is that it has an efficient open source implementation of rational univariate representations (see Fabrice Rouillier's research report for a description of this technique), but giac also provides a fairly convenient framework where to use multiprecision and interval arithmetic.
The program tests a very large number of inequalities, in number fields that are "small" extensions of the field of coefficients of the matrices. In the most complicated case, the degree of the number field is 24, so real equations for the faces have coefficients in a number field "only" of degree 12, but the "small" extensions can easily slow down the computer a lot!