Resultants of slice regular polynomials in two quaternionic variables

IF 1.3 4区计算机科学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer Aided Geometric Design Pub Date : 2024-08-21 DOI:10.1016/j.cagd.2024.102381

Anna Gori , Giulia Sarfatti , Fabio Vlacci

引用次数: 0

Abstract

We introduce a non-commutative resultant, for slice regular polynomials in two quaternionic variables, defined in terms of a suitable Dieudonné determinant. We use this tool to investigate the existence of common zeros and common factors of slice regular polynomials and we give a kinematic interpretation of our results.

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两个四元变量中切片正则多项式的结果项

我们为两个四元变量中的切片正多项式引入了一种非交换结果，它是根据合适的 Dieudonné 行列式定义的。我们利用这一工具来研究切片正则多项式的共零点和共因数的存在性，并给出了我们的结果的运动学解释。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computer Aided Geometric Design 工程技术-计算机：软件工程

CiteScore

3.50

自引率

13.30%

发文量

审稿时长

60 days

期刊介绍： The journal Computer Aided Geometric Design is for researchers, scholars, and software developers dealing with mathematical and computational methods for the description of geometric objects as they arise in areas ranging from CAD/CAM to robotics and scientific visualization. The journal publishes original research papers, survey papers and with quick editorial decisions short communications of at most 3 pages. The primary objects of interest are curves, surfaces, and volumes such as splines (NURBS), meshes, subdivision surfaces as well as algorithms to generate, analyze, and manipulate them. This journal will report on new developments in CAGD and its applications, including but not restricted to the following: -Mathematical and Geometric Foundations- Curve, Surface, and Volume generation- CAGD applications in Numerical Analysis, Computational Geometry, Computer Graphics, or Computer Vision- Industrial, medical, and scientific applications. The aim is to collect and disseminate information on computer aided design in one journal. To provide the user community with methods and algorithms for representing curves and surfaces. To illustrate computer aided geometric design by means of interesting applications. To combine curve and surface methods with computer graphics. To explain scientific phenomena by means of computer graphics. To concentrate on the interaction between theory and application. To expose unsolved problems of the practice. To develop new methods in computer aided geometry.