签名基础理论的公理

IF 0.6 4区数学 Q4 COMPUTER SCIENCE, THEORY & METHODS

Journal of Symbolic Computation Pub Date : 2023-12-18 DOI:10.1016/j.jsc.2023.102275

Pierre Lairez

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引用次数: 0

摘要

在发现 F5 算法 20 年后的今天，带有签名的格罗布纳基仍然难以理解，也难以适应不同的环境。这与布赫伯格算法形成了鲜明对比，布赫伯格算法的正确性和终止性显而易见，我们可以对其进行多向弯曲。我提出了一种带签名的格罗伯纳基的公理化方法，目的是解除理论与算法之间的耦合，给出适用于许多不同环境（如子模的格罗伯纳、F4 式还原、非交换环、非诺特环境等）的一般结果，并扩展签名算法的范围。

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Axioms for a theory of signature bases

Twenty years after the discovery of the F5 algorithm, Gröbner bases with signatures are still challenging to understand and to adapt to different settings. This contrasts with Buchberger's algorithm, which we can bend in many directions keeping correctness and termination obvious. I propose an axiomatic approach to Gröbner bases with signatures with the purpose of uncoupling the theory and the algorithms, giving general results applicable in many different settings (e.g. Gröbner for submodules, F4-style reduction, noncommutative rings, non-Noetherian settings, etc.), and extending the reach of signature algorithms.

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来源期刊

Journal of Symbolic Computation 工程技术-计算机：理论方法

CiteScore

2.10

自引率

14.30%

发文量

审稿时长

142 days

期刊介绍： An international journal, the Journal of Symbolic Computation, founded by Bruno Buchberger in 1985, is directed to mathematicians and computer scientists who have a particular interest in symbolic computation. The journal provides a forum for research in the algorithmic treatment of all types of symbolic objects: objects in formal languages (terms, formulas, programs); algebraic objects (elements in basic number domains, polynomials, residue classes, etc.); and geometrical objects. It is the explicit goal of the journal to promote the integration of symbolic computation by establishing one common avenue of communication for researchers working in the different subareas. It is also important that the algorithmic achievements of these areas should be made available to the human problem-solver in integrated software systems for symbolic computation. To help this integration, the journal publishes invited tutorial surveys as well as Applications Letters and System Descriptions.