Solvability by radicals from an algorithmic point of view

Authors:
G. Hanrot;F. Morain
Affiliations:
Project SPACE, INRIA Lorraine, Nancy Cedex, France;LIX, École Polytechnique, Palaiseau Cedex, France
Venue:
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Year:
2001

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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.