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Journals / Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi / 2026 / Cilt: 24 Sayı: 3

A New and Efficient Algorithm for Detecting Affine Equivalences and Symmetries of Ruled Rational Surfaces

Rasyonel Regle Yüzeylerin Afin Denklikleri ve Simetrilerinin Tespiti Üzerine Yeni ve Etkili Bir Algoritma

Hüsnü Anil Çoban(KARADENİZ TEKNİK ÜNİVERSİTESİ)0000-0001-8175-4960
Uğur Gözütok(MİLLİ SAVUNMA ÜNİVERSİTESİ)0000-0002-6072-3134
Pages
574–582
Publication Date
2024-06-27
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AI Summary & Key Takeaways

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

The performance of the method was thoroughly tested using the Maple^TM (2021) computer algebra system after it had been transformed into an algorithm.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:A novel and efficient method for computing all affine equivalences between two ruled surfaces using rational parameterizations is presented in this paper.
📊
Key Findings & Data:The technique essentially uses affine differential invariants to find equivalences in contrast to other methods, our method does not require polynomial system solutions, which complicate computations and increase computation time.
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Conclusion & Impact:The performance of the method was thoroughly tested using the Maple^TM (2021) computer algebra system after it had been transformed into an algorithm.
🔬Design:Araştırma Makalesi
📍Scope:2021 Verileri
⚙️Variables:Regle yüzeyler · Afin denklik · Afin simetri

Abstract

A novel and efficient method for computing all affine equivalences between two ruled surfaces using rational parameterizations is presented in this paper. The technique essentially uses affine differential invariants to find equivalences in contrast to other methods, our method does not require polynomial system solutions, which complicate computations and increase computation time. The performance of the method was thoroughly tested using the Maple^TM (2021) computer algebra system after it had been transformed into an algorithm.

Özet

Bu çalışmada, rasyonel parametrizasyonlar yardımıyla verilen iki regle yüzey arasındaki tüm afin denklikleri hesaplayan yeni ve etkili bir yöntem sunulmaktadır. Yöntem, temelde, afin diferansiyel invaryantları kullanılarak denklikleri tespit etmektedir. Bu sayede, benzer problemi çözen metotlardan farklı olarak hesaplamayı zorlaştıran ve hesaplama süresinin uzamasına sebep olan polinom sistemi çözümlerine ihtiyaç duymamaktadır. Bu yöntem bir algoritma haline getirilmiş ve yöntemin performansı Maple^TM (2021) bilgisayar cebir sistemi kullanılarak, geniş kapsamlı testlerle incelenmiştir.

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Cite This Article

Çoban, H. A., Gözütok, U. (2024). A New and Efficient Algorithm for Detecting Affine Equivalences and Symmetries of Ruled Rational Surfaces. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, Cilt: 24 Sayı: 3, 574–582. https://doi.org/10.35414/akufemubid.1374733

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References (14)

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