Detecting isometries and symmetries of implicit algebraic surfaces

Uğur Gözütok; Hüsnü Anıl Çoban; Uğur Gözütok; Hüsnü Anıl Çoban

doi:10.3934/math.2024212

AIMS Mathematics

2024, Volume 9, Issue 2: 4294-4308. doi: 10.3934/math.2024212

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Detecting isometries and symmetries of implicit algebraic surfaces

Uğur Gözütok ^{1
,
,},
Hüsnü Anıl Çoban ²

1.
Department of Natural Sciences, National Defence University, İstanbul, Türkiye
2.
Department of Mathematics, Karadeniz Technical University, Trabzon, Türkiye

Received: 06 November 2023 Revised: 05 January 2024 Accepted: 09 January 2024 Published: 16 January 2024
MSC : 14Q10, 14Q20

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.
- implicit surfaces,
- isometries,
- symmetries,
- equivalences,
- computer algebra
Citation: Uğur Gözütok, Hüsnü Anıl Çoban. Detecting isometries and symmetries of implicit algebraic surfaces[J]. AIMS Mathematics, 2024, 9(2): 4294-4308. doi: 10.3934/math.2024212

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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.

References

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