Computing direct sum decompositions

IF 1.1 4区数学 Q4 COMPUTER SCIENCE, THEORY & METHODS

Journal of Symbolic Computation Pub Date : 2025-08-14 DOI:10.1016/j.jsc.2025.102486

Devlin Mallory , Mahrud Sayrafi

引用次数: 0

Abstract

We describe and prove correctness of two practical algorithms for finding indecomposable summands of finitely generated modules over a finitely generated k-algebra R. The first algorithm applies in the (multi)graded case, which enables the computation of indecomposable summands of coherent sheaves on subvarieties of toric varieties (in particular, for varieties embedded in projective space); the second algorithm applies when R is local and k is a finite field, opening the door to computing decompositions in singularity theory. We also present multiple examples, including some which present previously unknown phenomena regarding the behavior of summands of Frobenius pushforwards (including in the non-graded case) and syzygies over Artinian rings.

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计算直接和分解

我们描述并证明了在有限生成k代数r上求有限生成模的不可分解和的两种实用算法的正确性。第一种算法适用于（多）梯度情况，它使得在环变的子变（特别是嵌入在射影空间中的变）上求相干束的不可分解和成为可能；第二种算法适用于R是局部的，k是有限域的情况，打开了奇异理论中计算分解的大门。我们还提出了多个例子，包括一些关于Frobenius推进的求和行为（包括在非分级情况下）和阿提尼安环上的合子的以前未知的现象。

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.