HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Conference papers

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.
Document type :
Conference papers
Complete list of metadata

Contributor : Publications Loria Connect in order to contact the contributor
Submitted on : Tuesday, September 26, 2006 - 2:46:51 PM
Last modification on : Friday, February 4, 2022 - 3:31:54 AM


  • HAL Id : inria-00100542, version 1



Guillaume Hanrot, François Morain. Solvability by radicals from an algorithmic point of view. International Symposium on Symbolic and Algebraic Computation - ISSAC'2001, 2001, London, Ontario, Canada, 18 p. ⟨inria-00100542⟩



Record views