线性微分系统微分伽罗瓦群的李代数计算

Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation Pub Date : 2016-07-20 DOI:10.1145/2930889.2930932

M. Barkatou, T. Cluzeau, Jacques-Arthur Weil, L. D. Vizio

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引用次数: 12

摘要

我们考虑一个线性微分系统[a]: y'= a, y}，其中a在C(x)中有系数。[A]的微分伽罗瓦群G是测量解间代数关系的线性代数群。虽然存在计算$G$的通用算法，但没有一个是实用的或可实现的。本文提出了在[A]绝对不可约时计算g的李代数g的一种算法。该算法在Maple中实现。

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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Computing the Lie Algebra of the Differential Galois Group of a Linear Differential System

We consider a linear differential system [A] : y'=A, y}, where A has with coefficients in C(x). The differential Galois group G of [A] is a linear algebraic group which measures the algebraic relations among solutions. Although there exist general algorithms to compute $G$, none of them is either practical or implemented. This paper proposes an algorithm to compute the Lie algebra g of G when [A] is absolutely irreducible. The algorithm is implemented in Maple.

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Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation

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