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Research Article | Open Access

Detecting isometries and symmetries of implicit algebraic surfaces

Uğur Gözütok1( ), Hüsnü Anıl Çoban2
Department of Natural Sciences, National Defence University, İstanbul, Türkiye
Department of Mathematics, Karadeniz Technical University, Trabzon, Türkiye
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Abstract

We presented a new and complete algorithm for detecting isometries and symmetries of implicit algebraic surfaces. First, our method reduced the problem to the case of isometries fixing the origin. Second, using tools from elimination theory and polynomial factoring, we determined the desired isometries between the surfaces. We have implemented the algorithm in Maple to provide evidences of the efficiency of the method.

Keywords

implicit surfacesisometriessymmetriesequivalencescomputer algebra
CLC number: 14Q10, 14Q20

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AIMS Mathematics
Volume 9 Issue 2,
February 2024
Pages 4294-4308
DOI: 10.3934/math.2024212

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Cite this article:
Gözütok U, Çoban HA. Detecting isometries and symmetries of implicit algebraic surfaces. AIMS Mathematics, 2024, 9(2): 4294-4308. https://doi.org/10.3934/math.2024212

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Received: 06 November 2023
Revised: 05 January 2024
Accepted: 09 January 2024
Published: 15 February 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)