线性泛函系统的Picard—Vessiot扩展

Proceedings of the 2005 international symposium on Symbolic and algebraic computation Pub Date : 2005-07-24 DOI:10.1145/1073884.1073896

M. Bronstein, Ziming Li, Min Wu

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引用次数: 28

摘要

常微分方程和差分方程的皮卡德-维西奥扩展是众所周知的，并且是相关伽罗瓦理论的核心。本文构造了线性维数有限的线性偏泛函方程组的基本矩阵和Picard-Vessiot扩展。然后，我们利用这些扩展证明了这样一个系统的一个因子的所有解都可以被原系统的解补全。

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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Picard--Vessiot extensions for linear functional systems

Picard-Vessiot extensions for ordinary differential and difference equations are well known and are at the core of the associated Galois theories. In this paper, we construct fundamental matrices and Picard-Vessiot extensions for systems of linear partial functional equations having finite linear dimension. We then use those extensions to show that all the solutions of a factor of such a system can be completed to solutions of the original system.

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Proceedings of the 2005 international symposium on Symbolic and algebraic computation

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