Generic Gröbner basis of a parametric ideal and its application to a comprehensive Gröbner system

IF 0.6 4区工程技术 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Applicable Algebra in Engineering Communication and Computing Pub Date : 2023-08-03 DOI:10.1007/s00200-023-00620-8

Katsusuke Nabeshima

引用次数: 0

Abstract

A relationship between a parametric ideal and its generic Gröbner basis is discussed, and a new stability condition of a Gröbner basis is given. It is shown that the ideal quotient of the parametric ideal by the ideal generated using the generic Gröbner basis provides the stability condition. Further, the stability condition is utilized to compute a comprehensive Gröbner system, and hence as an application, we obtain a new algorithm for computing comprehensive Gröbner systems. The proposed algorithm has been implemented in the computer algebra system Risa/Asir and experimented with a number of examples. Its performance (execution timings) has been compared with the Kapur-Sun-Wang’s algorithm for computing comprehensive Gröbner systems.

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参数理想的一般Gröbner基础及其在综合Gröbner系统中的应用

讨论了参数理想和它的通用格罗伯纳基之间的关系，并给出了格罗伯纳基的一个新的稳定性条件。研究表明，参数理想的理想商和使用通用格罗布纳基生成的理想提供了稳定性条件。此外，我们还利用该稳定性条件计算了综合格罗伯纳系统，并由此获得了计算综合格罗伯纳系统的新算法。提出的算法已在计算机代数系统 Risa/Asir 中实现，并用大量实例进行了实验。其性能（执行时间）已与计算综合格罗伯纳系统的 Kapur-Sun-Wang 算法进行了比较。

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

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.