Solvability by radicals from an algorithmic point of view
Identifieur interne : 009571 ( Main/Exploration ); précédent : 009570; suivant : 009572Solvability by radicals from an algorithmic point of view
Auteurs : Guillaume Hanrot [France] ; François Morain [France]Source :
English descriptors
- mix :
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.
Url:
Affiliations:
- France
- Grand Est, Lorraine (région)
- Nancy
- Institut national polytechnique de Lorraine, Université Nancy 2, Université de Lorraine
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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.</div></front></TEI><affiliations><list><country><li>France</li></country><region><li>Grand Est</li><li>Lorraine (région)</li></region><settlement><li>Nancy</li></settlement><orgName><li>Institut national polytechnique de Lorraine</li><li>Université Nancy 2</li><li>Université de Lorraine</li></orgName></list><tree><country name="France"><region name="Grand Est"><name sortKey="Hanrot, Guillaume" sort="Hanrot, Guillaume" uniqKey="Hanrot G" first="Guillaume" last="Hanrot">Guillaume Hanrot</name></region><name sortKey="Morain, Francois" sort="Morain, Francois" uniqKey="Morain F" first="François" last="Morain">François Morain</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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