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Solvability by Radicals from an Algorithmic Point of View

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.
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Submitted on : Wednesday, May 24, 2006 - 10:10:54 AM
Last modification on : Friday, February 4, 2022 - 3:30:27 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:11:44 PM


  • HAL Id : inria-00072522, version 1



Guillaume Hanrot, François Morain. Solvability by Radicals from an Algorithmic Point of View. [Research Report] RR-4109, INRIA. 2001. ⟨inria-00072522⟩



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