𝐕𝐢𝐧𝐧𝐲 𝐭𝐡𝐞 𝐜𝐨𝐱𝐛𝐨𝐲

Learning to herd Coxeter diagrams in the Hyperbolic Plains since 2021

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Port of aperep/vinberg-algorithm to julia with some changes

Warning. The code is still being tested, and surely has many bugs!

Description

• The finite volume check for Coxeter diagrams is implemented “from scratch” using Guglielmetti's thesis as theoretical resource and CoxIter as a comparison point (plus a majority of tests from there); thank you!
• The main bulk of Vinberg's algorithm (and associated procedures) is ported (modulo errors introduced in the process) from B&P.
• The code uses static bitsets for hopefully efficient storage of small integer sets. The code for this comes from here. TODO. Contact the author to ask if we can use their code, and under what licence (see here).

How to use

• If not already installed, run julia install_packages.jl to install the packages used in the code.
• Go to the root folder of the project (having subfolder lattices,graphs,src).
• Launch julia with julia -t auto to enable multithreading (might be useful, but on small examples does't look like it is)
• call include("src/vinberg.jl").
• calling toggle(true) or toggle(false) respectively enables/disables a majority of asserts in the code.

Now everything needed is loaded.

• To run the Vinberg Algorithm on a lattice given by a matrix M, call Vinberg_Algorithm(M).
• Some matrices are accessible through the dictionary L, for instance L["Vin07_L1"] contains one matrix of Vinberg.