Elementary Möbius Geometry

The software consists of three Mathematica Notebooks and a collection moebpack.tar.gz of nine Mathematica packages needed for interactive working with the notebooks or developing new notebooks in this field. The aim is to calculate the Möbius invariants of pairs of a k- and an l-sphere in the n-dimensional Möbius space, its relations to the corresponding Euclidean invariants (Coxeter invariant and generalizations), visualisation of the corresponding configurations of spheres and circles. The packages contain tools of Euclidean and pseudo-Euclidean geometry as well as elements of Lie algebras. In particular, an orthogonalization procedure for vectors in a finite dimensional pseudo-Euclidean vector space is given, generalizing Erhard Schmidt’s orthogonalization.

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