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Journals / Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi / 2023 / Cilt: 39 Sayı: 2

Computing Isometries and Symmetries of Implicit Plane Algebraic Curves

Kapalı Formda Temsil Edilen Cebirsel Düzlem Eğrilerinin İzometrileri ve Simetrilerinin Hesaplanması

Hüsnü Anil ÇOBAN
Uğur GÖZÜTOK
Pages
303–314
Publication Date
2023-08-31
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We have implemented the algorithm in the computer algebra system Maple to run tests providing evidences of the efficiency of the method.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, we present a new and efficient algorithm to compute the isometries and symmetries of implicit plane algebraic curves.
📊
Key Findings & Data:The method to be constructed in the article consists of two parts.
💡
Conclusion & Impact:We have implemented the algorithm in the computer algebra system Maple to run tests providing evidences of the efficiency of the method.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Cebirsel eğriler · İzometriler · Simetriler

Abstract

In this study, we present a new and efficient algorithm to compute the isometries and symmetries of implicit plane algebraic curves. The method to be constructed in the article consists of two parts. The first part of the method reduces the problem to isometries fixing the origin, while the other part determines the isometries between the curves. If the input curves are identical, the method detects all the symmetries of an implicit plane algebraic curve. We have implemented the algorithm in the computer algebra system Maple to run tests providing evidences of the efficiency of the method.

Özet

Bu çalışmada, kapalı formda temsil edilen cebirsel düzlem eğrilerinin izometrilerinin ve simetrilerinin hesaplanması için yeni ve etkili bir algoritma sunulmaktadır. Makalede inşa edilecek metot iki kısımdan oluşmaktadır. Metodun birinci kısmı, problemi, orijini sabitleyen izometrilere indirgerken, diğer kısımda eğrilerin denk olmasını sağlayan izometrilerin tespiti yapılmaktadır. Girdi eğrilerinin özdeş olması durumunda metot, kapalı formda temsil edilen bir cebirsel düzlem eğrisinin tüm simetrilerini tespit etmektedir. Metodun etkinliğine kanıt oluşturacak testler yürütülmesi için, oluşturulan algoritma, Maple bilgisayar cebir sistemi kullanılarak implement edilmiştir.

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Cite This Article

ÇOBAN, H. A., GÖZÜTOK, U. (2023). Computing Isometries and Symmetries of Implicit Plane Algebraic Curves. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi, Cilt: 39 Sayı: 2, 303–314. https://ajindex.com/articles/960419

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