Sasbi-standard bases of modules

IF 0.9 4区数学 Q4 COMPUTER SCIENCE, THEORY & METHODS

Journal of Symbolic Computation Pub Date : 2026-05-01 Epub Date: 2025-10-14 DOI:10.1016/j.jsc.2025.102522

Nazia Jabeen, Junaid Alam Khan

引用次数: 0

Abstract

The theory of Standard bases of modules over the localization of a polynomial ring (with respect to a local ordering >) is well-developed. For a polynomial subalgebra A, the concept of “Subalgebra bases” of

A_{>}

(localization of A with respect to >) is well-defined, known as Sasbi bases (subalgebra analogue of Standard bases for ideals). In this paper, we have developed and proposed a theory for Standard bases of modules over

A_{>}

(admitting a finite Sasbi basis), termed as Sasbi-Standard bases. The main goal is to develop a constructive algorithm for the computation of these bases, which we implement in the computer algebra system SINGULAR. We also present an application of these bases to compute singularity invariants: the monoid of values of an algebroid curve and the monomodule of values of the Kähler's differentials.

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sasbi标准的模块基础

多项式环的局部化上模的标准基理论（关于局部序）得到了很好的发展。对于多项式子代数a， A>的“子代数基”（a相对于>的局部化）的概念是定义良好的，称为Sasbi基（理想标准基的子代数模拟）。在本文中，我们发展并提出了A>上模块的标准基理论（承认有限的Sasbi基），称为Sasbi-标准基。本文的主要目标是开发一种计算这些基的构造算法，并在计算机代数系统SINGULAR中实现。我们也给出了这些基在计算奇异不变量的一个应用：代数曲线的值的单模和Kähler的微分值的单模。

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.