零维理想noether算子的有效计算算法

IF 0.6 4区工程技术 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Applicable Algebra in Engineering Communication and Computing Pub Date : 2022-08-08 DOI:10.1007/s00200-022-00570-7

Katsusuke Nabeshima, Shinichi Tajima

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引用次数: 0

摘要

我们在符号计算的背景下考虑Noetherian算子。利用完整的\({\mathcal D}\) -模理论，提出了一种计算零维理想Noetherian算子的新方法。提出了一种主要由线性代数技术组成的有效算法来计算它们。此外，作为应用，讨论了利用noether算子计算多项式理想的新方法。

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Effective algorithm for computing Noetherian operators of zero-dimensional ideals

We consider Noetherian operators in the context of symbolic computation. Upon utilizing the theory of holonomic \({\mathcal D}\)-modules, we present a new method for computing Noetherian operators associated to a zero-dimensional ideal. An effective algorithm that consists mainly of linear algebra techniques is proposed for computing them. Moreover, as applications, new computation methods of polynomial ideals are discussed by utilizing the Noetherian operators.

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来源期刊

Applicable Algebra in Engineering Communication and Computing 工程技术-计算机：跨学科应用

CiteScore

2.90

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Algebra is a common language for many scientific domains. In developing this language mathematicians prove theorems and design methods which demonstrate the applicability of algebra. Using this language scientists in many fields find algebra indispensable to create methods, techniques and tools to solve their specific problems. Applicable Algebra in Engineering, Communication and Computing will publish mathematically rigorous, original research papers reporting on algebraic methods and techniques relevant to all domains concerned with computers, intelligent systems and communications. Its scope includes, but is not limited to, vision, robotics, system design, fault tolerance and dependability of systems, VLSI technology, signal processing, signal theory, coding, error control techniques, cryptography, protocol specification, networks, software engineering, arithmetics, algorithms, complexity, computer algebra, programming languages, logic and functional programming, algebraic specification, term rewriting systems, theorem proving, graphics, modeling, knowledge engineering, expert systems, and artificial intelligence methodology. Purely theoretical papers will not primarily be sought, but papers dealing with problems in such domains as commutative or non-commutative algebra, group theory, field theory, or real algebraic geometry, which are of interest for applications in the above mentioned fields are relevant for this journal. On the practical side, technology and know-how transfer papers from engineering which either stimulate or illustrate research in applicable algebra are within the scope of the journal.