Displaying similar documents to “Computation of the Galois group of a polynomial with rational coefficients.”

Differential equations and algebraic transcendents: french efforts at the creation of a Galois theory of differential equations 1880–1910

Tom Archibald (2011)

Revue d'histoire des mathématiques

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A “Galois theory” of differential equations was first proposed by Émile Picard in 1883. Picard, then a young mathematician in the course of making his name, sought an analogue to Galois’s theory of polynomial equations for linear differential equations with rational coefficients. His main results were limited by unnecessary hypotheses, as was shown in 1892 by his student Ernest Vessiot, who both improved Picard’s results and altered his approach, leading Picard to assert that his lay...

Differential Galois realization of double covers

Teresa Crespo, Zbigniew Hajto (2002)

Annales de l’institut Fourier

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An effective construction of homogeneous linear differential equations of order 2 with Galois group 2 A 4 , 2 S 4 or 2 A 5 is presented.

On the inverse problem of Galois theory.

Núria Vila (1992)

Publicacions Matemàtiques

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The problem of the construction of number fields with Galois group over Q a given finite groups has made considerable progress in the recent years. The aim of this paper is to survey the current state of this problem, giving the most significant methods developed in connection with it.