On the computation of Gröbner bases for matrix-weighted homogeneous systems

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

Journal of Symbolic Computation Pub Date : 2024-04-05 DOI:10.1016/j.jsc.2024.102327

Thibaut Verron

引用次数: 0

Abstract

In this paper, we examine the structure of systems that are weighted homogeneous for several systems of weights, and how it impacts the computation of Gröbner bases. We present several linear algebra algorithms for computing Gröbner bases for systems with this structure, either directly or by reducing to existing structures. We also present suitable optimization techniques.

As an opening towards complexity studies, we discuss potential definitions of regularity and prove that they are generic if non-empty. Finally, we present experimental data from a prototype implementation of the algorithms in SageMath.

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论矩阵加权均质系统的格罗布纳基计算

在本文中，我们研究了多个权重系统的加权同质系统结构，以及它如何影响格罗伯纳基的计算。我们提出了几种线性代数算法，用于直接或通过还原现有结构计算具有这种结构的系统的格氏基。作为复杂性研究的开端，我们讨论了正则性的潜在定义，并证明它们在非空的情况下是通用的。最后，我们介绍了在 SageMath 中实现算法原型的实验数据。

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

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.