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

被引：9

作者：

Barkatou, Moulay ^{[1
]}

Cluzeau, Thomas ^{[1
]}

Weil, Jacques-Arthur ^{[1
]}

Di Vizio, Lucia ^{[2
]}

机构：

[1] Univ Limoges, CNRS, XLIM UMR 7252, 123 Av Albert Thomas, F-87060 Limoges, France

[2] Univ Versailles St Quentin En Yvelines, Math Lab, UMR 8100, 45 Av Etats Unis, F-78035 Versailles, France

来源：

PROCEEDINGS OF THE 2016 ACM INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION (ISSAC 2016) | 2016年

关键词：

Computer algebra; Algorithms; Linear differential systems; Differential Galois theory; Lie algebras; Grothendieck-Katz p-curvature conjecture; Eigenrings; Reduced forms; REDUCIBILITY; OPERATORS;

D O I：

10.1145/2930889.2930932

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We consider a linear differential system [A] : y' = A y 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.

引用

页码：63 / 70

页数：8

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