Software for sporadic triangle groups
The goal of this page is to distribute software that performs the verifications needed in my paper with Julien Paupert and John Parker.
Besides performing the verifications needed in our paper, it produced the pictures of our fundamental domains that appear in this poster.
In order to run the program, you should
In order to compile the program, you will need to install
On Mac OS systems, it should work simply to run the ./compile_mac script after installing giac (see also the giac documentation for more info. So far I have not been able to compile spocheck on MacOS 10.9, but it compiles in earlier versions (version 10.6 and 10.7 seem OK). If you have trouble running spocheck with your version, you may need to recompile giac for your machine.
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! This seems to make the program crash on some computers (only for the group 4s5, as far as I am aware).