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CoxIter – computing invariants of hyperbolic Coxeter groups. (English) Zbl 1333.20040

Summary: CoxIter is a computer program designed to compute invariants of hyperbolic Coxeter groups. Given such a group, the program determines whether it is cocompact or of finite covolume, whether it is arithmetic in the non-cocompact case, and whether it provides the Euler characteristic and the combinatorial structure of the associated fundamental polyhedron. The aim of this paper is to present the theoretical background for the program. The source code is available online as supplementary material with the published article and on the author’s website [http://coxiter.rgug.ch].

MSC:

20F55 Reflection and Coxeter groups (group-theoretic aspects)
20-04 Software, source code, etc. for problems pertaining to group theory
51-04 Software, source code, etc. for problems pertaining to geometry
20F67 Hyperbolic groups and nonpositively curved groups
51F15 Reflection groups, reflection geometries
22E40 Discrete subgroups of Lie groups
52B05 Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.)

Software:

CoxIter
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References:

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