Related papers: Splitting differential equations using Galois theo…

An algebraic technique is presented that does not use results of model theory and makes it possible to construct a general Galois theory of arbitrary nonlinear systems of partial differential equations. The algebraic technique is based on…

We develop a Galois theory for linear differential equations equipped with the action of an endomorphism. This theory is aimed at studying the difference algebraic relations among the solutions of a linear differential equation. The Galois…

We make explicit certain results around the Galois correspondence in the context of definable automorphism groups, and point out the relation to some recent papers dealing with the Galois theory of algebraic differential equations when the…

This article is interested in internality to the constants of systems of autonomous algebraic ordinary differential equations. Roughly, this means determining when can all solutions of such a system be written as a rational function of…

We extend and apply the Galois theory of linear differential equations equipped with the action of an endomorphism. The Galois groups in this Galois theory are difference algebraic groups and we use structure theorems for these groups to…

The Galois theory of logarithmic differential equations with respect to relative D-groups in partial differential-algebraic geometry is developed.

This article is on the inverse Galois problem in Galois theory of linear iterative differential equations in positive characteristic. We show that it has an affirmative answer for reduced algebraic group schemes over any iterative…

We present a theory for splitting algebras of monic polynomials over rings, and apply the results to symmetric functions, and Galois theory. Our main result is that the ring of invariants of a splitting algebra under the symmetric group…

We introduce a novel integrability-preserving discretization for a broad class of differential equations with variable coefficients, encompassing both linear and nonlinear cases. The construction is achieved via a categorical approach that…

In this article, we realize some groups as Galois groups over rational numbers and finite extension of rational numbers by studying right splitting of some exact sequences, Galois correspondence and algebraic operations on Galois…

A categorical theory for the discretization of a large class of dynamical systems with variable coefficients is proposed. It is based on the existence of covariant functors between the Rota category of Galois differential algebras and…

In this paper, we present methods to simplify reducible linear differential systems before solving. Classical integrals appear naturally as solutions of such systems. We will illustrate the methods developed in a previous paper on several…

Galois theory is developed using elementary polynomial and group algebra. The method follows closely the original prescription of Galois, and has the benefit of making the theory accessible to a wide audience. The theory is illustrated by a…

In this paper, we explain how to compute the Lie algebra of the differential Galois group of a reducible linear differential system. We achieve this by showing how to transform a block-triangular linear differential system into a…

We develop a Galois theory for systems of linear difference equations with an action of an endomorphism {\sigma}. This provides a technique to test whether solutions of such systems satisfy {\sigma}-polynomial equations and, if yes, then…

We develop a Galois theory for systems of linear difference equations with periodic parameters, for which we also introduce linear difference algebraic groups. We then apply this to constructively test if solutions of linear q-difference…

We study the inverse problem in the difference Galois theory of linear differential equations over the difference-differential field $\mathbb{C}(x)$ with derivation $\frac{d}{dx}$ and endomorphism $f(x)\mapsto f(x+1)$. Our main result is…

We apply the differential Galois theory for difference equations developed by Hardouin and Singer to compute the differential Galois group for a second-order linear $q$-difference equation with rational function coefficients. This Galois…

We present a Galois theory of parameterized linear differential equations where the Galois groups are linear differential algebraic groups, that is, groups of matrices whose entries are functions of the parameters and satisfy a set of…

We present a Galois theory of difference equations designed to measure the differential dependencies among solutions of linear difference equations. With this we are able to reprove Hoelder's Theorem that the Gamma function satisfies no…