Elie Compoint

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At present we do not know a general algorithm that will compute the Galois group of a linear differential equation with coefficients in a differential field k, even when k = Q̄(x), where Q̄ is the algebraic closure of the rational numbers. In contrast, algorithms for calculating the Galois group of a polynomial with coefficients in Q or Q̄(x) have been(More)
A differential system [A] : Y ′ = AY , with A ∈ Mat(n, k) is said to be in reduced form if A ∈ g(k) where g is the Lie algebra of the differential Galois group G of [A]. In this article, we give a constructive criterion for a system to be in reduced form. When G is reductive and unimodular, the system [A] is in reduced form if and only if all of its(More)
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