Linear systems of Diophantine equations

IF 0.7 4区 数学 Q2 Mathematics
F. Szechtman
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引用次数: 0

Abstract

Given free modules $M\subseteq L$ of finite rank $f\geq 1$ over a principal ideal domain $R$, we give a procedure to construct a basis of $L$ from a basis of $M$ assuming the invariant factors or elementary divisors of $L/M$ are known. Given a matrix $A\in M_{m,n}(R)$ of rank $r$, its nullspace $L$ in $R^n$ is a free $R$-module of rank $f=n-r$. We construct a free submodule $M$ of $L$ of rank $f$ naturally associated with $A$ and whose basis is easily computable, we determine the invariant factors of the quotient module $L/M$ and then indicate how to apply the previous procedure to build a basis of $L$ from one of $M$.
丢番图方程的线性系统
给定主理想域$R$上有限秩$f\geq 1$的自由模$M\subseteq L$,在假设$L/M$的不变因子或初等因子已知的情况下,给出了从$M$的基构造$L$的基的过程。给定一个秩为$r$的矩阵$A\in M_{m,n}(R)$,其在$R^n$中的零空间$L$是秩为$f=n-r$的自由$R$ -模块。我们构造了$L$的自由子模块$M$,其秩$f$与$A$自然相关,其基易于计算,我们确定了商模块$L/M$的不变因子,然后指出如何应用前面的过程从$M$的一个构建$L$的基。
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
CiteScore
1.20
自引率
14.30%
发文量
45
审稿时长
6-12 weeks
期刊介绍: The journal is essentially unlimited by size. Therefore, we have no restrictions on length of articles. Articles are submitted electronically. Refereeing of articles is conventional and of high standards. Posting of articles is immediate following acceptance, processing and final production approval.
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