MoebInv: C++ libraries for manipulations in non-Euclidean geometry

Abstract

The introduced package MoebInv contains two C ++ libraries for symbolic, numeric and graphical manipulations in non-Euclidean geometry. The first library cycle implements basic geometric operations on cycles, which are the zero sets of certain polynomials of degree two. The second library figure operates on ensembles of cycles interconnected by Moebius-invariant relations: orthogonality, tangency, etc. Both libraries work in spaces with any dimension and arbitrary signatures of their metrics. Their essential functionality is accessible in interactive modes from Python/Jupyter shells and a dedicated Graphical User Interface. The latter does not require any coding skills and can be used in education. The package is tested on (and supplied for) various Linux distributions, Windows 10, Mac OS X and several cloud services.

Cycles Cross Ratio: an Invitation

“…The above condition is necessary, we describe a sufficient one as a figure in the sense of [22][23][24]. In short, a figure is an ensemble of cycles interrelated by cycles'…”

“…There is an interactive version of this paper implemented as a Jupyter notebook [25] based on the MoebInv software package [24].…”