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1 SPACES - Solving problems through algebraic computation and efficient software INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications 2 LIX - Laboratoire d-informatique de l-École polytechnique Palaiseau

Abstract : Any textbook on Galois theory contains a proof that a polynomial equation with solvable Galois group can be solved by radicals. From a practical point of view, we need to find suitable representations of the group and the roots of the polynomial. We first reduce the problem to that of cyclic extensions of prime degree and then work out the radicals, using the work of Girstmair. We give numerical examples of Abelian and non-Abelian solvable equations and apply the general framework to the construction of Hilbert Class fields of imaginary quadratic fields.

Keywords : GALOIS THEORY SOLVABILITY BY RADICALS





Author: Guillaume Hanrot - François Morain -

Source: https://hal.archives-ouvertes.fr/



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