✦ LIBER ✦

Computing Galois Groups of Completely Reducible Differential Equations

✍ Scribed by Elie Compoint; Michael F Singer

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 449 KB
Volume: 28
Category: Article
ISSN: 0747-7171
DOI: 10.1006/jsco.1999.0311

No coin nor oath required. For personal study only.

✦ Synopsis

We give an algorithm to calculate a presentation of the Picard-Vessiot extension associated to a completely reducible linear differential equation (i.e. an equation whose Galois group is reductive). Using this, we show how to compute the Galois group of such an equation as well as properties of the Galois groups of general equations.

📜 SIMILAR VOLUMES

Galois Theory of Differential Equations,

Galois Theory of Differential Equations, Algebraic Groups and Lie Algebras

✍ Marius van der Put 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 499 KB

On Reducible Linear Functional Different

On Reducible Linear Functional Differential Equations of Mixed Type

✍ Zhanyuan Hou 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 266 KB 👁 1 views

There are occasions when a linear autonomous functional differential equation of mixed type can be reduced to a neutral or retarded equation. A necessary condition for such reducibility is shown to be that the set of solutions of the characteristic equation is bounded on the right in the complex pla

Primitive Unimodular Groups of Degree 2

Primitive Unimodular Groups of Degree 2 as Differential Galois Groups

✍ Teresa Crespo; Zbigniew Hajto 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 143 KB

The construction starts with a polynomial with Galois group the given group and is based on representation theory.

Complete Symmetry Groups of Ordinary Dif

Complete Symmetry Groups of Ordinary Differential Equations and Their Integrals: Some Basic Considerations

✍ K. Andriopoulos; P.G.L. Leach; G.P. Flessas 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 116 KB

The concept of the complete symmetry group of a differential equation introduced by J. Krause (1994, J. Math. Phys. 35, 5734-5748) is extended to integrals of such equations. This paper is devoted to some aspects characterising complete symmetry groups. The algebras of the symmetries of both differe

Reducing the computational requirements

Reducing the computational requirements of the differential quadrature method

✍ Wen Chen; Yongxi Yu; Xinwei Wang 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 603 KB

This article shows that the weighting coefficient matrices of the differential quadrature method (DQM) are centrosymmetric or skew-centrosymmetric, if the grid spacings are symmetric irrespective of whether they are equal or unequal. A new skew centrosymmetric matrix is also discussed. The applicati

Symbolic Computation on Complex Polynomi

Symbolic Computation on Complex Polynomial Solution of Differential Equations

✍ Jun Zhang 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 447 KB

A symbolic computation scheme, based on the Lanczos τ -method, is proposed for obtaining exact polynomial solutions to some perturbed differential equations with suitable boundary conditions. The automated τ -method uses symbolic Faber polynomials as the perturbation terms for arbitrary circular sec