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

TL;DR

MoebInv is a versatile C++ library suite enabling symbolic, numeric, and graphical manipulations in non-Euclidean geometry, accessible via Python and GUI for educational and research purposes.

Contribution

It introduces two comprehensive C++ libraries for geometric operations on cycles and their relations in arbitrary non-Euclidean spaces, with multi-platform support and user-friendly interfaces.

Findings

Works in any dimension and metric signature.

Accessible through Python/Jupyter and GUI without coding.

Supported on major operating systems and cloud services.

Abstract

The introduced package MoebInv contains two CPP 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.