Kisil, VV orcid.org/0000-0002-6593-6147 (2019) An extension of Mobius--Lie geometry with conformal ensembles of cycles and its implementation in a GiNaC library. Proceedings of the International Geometry Center, 11 (3). pp. 45-67. ISSN 2072-9812
Abstract
We propose to consider ensembles of cycles (quadrics), which are interconnected through conformal-invariant geometric relations (e.g. “to be orthogonal”, “to be tangent”, etc.), as new objects in an extended Möbius–Lie geometry. It was recently demonstrated in several related papers, that such ensembles of cycles naturally parameterize many other conformally-invariant families of objects, e.g. loxodromes or continued fractions. The paper describes a method, which reduces a collection of conformally invariant geometric relations to a system of linear equations, which may be accompanied by one fixed quadratic relation. To show its usefulness, the method is implemented as a C++ library. It operates with numeric and symbolic data of cycles in spaces of arbitrary dimensionality and metrics with any signatures. Numeric calculations can be done in exact or approximate arithmetic. In the two- and three-dimensional cases illustrations and animations can be produced. An interactive Python wrapper of the library is provided as well.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This is an open access article under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. |
Keywords: | Lie–Möbius geometry |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 21 Dec 2015 12:42 |
Last Modified: | 03 Dec 2019 06:28 |
Status: | Published |
Publisher: | Odessa National Academy Food Technologies |
Identification Number: | 10.15673/tmgc.v11i3.1203 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:92845 |