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2006
Springer

A Modular Method for Computing the Splitting Field of a Polynomial

10 years 3 months ago
A Modular Method for Computing the Splitting Field of a Polynomial
We provide a modular method for computing the splitting field Kf of an integral polynomial f by suitable use of the byproduct of computation of its Galois group Gf by p-adic Stauduhar's method. This method uses the knowledge of Gf with its action on the roots of f over p-adic number field, and it reduces the computation of Kf to solving systems of linear equations modulo some power of the chosen prime p. We provide a careful treatment on reducing computational difficulty. We examine the ability/practicality of the method by experiments on a real computer and we study its complexity.
Guénaël Renault, Kazuhiro Yokoyama
Added 20 Aug 2010
Updated 20 Aug 2010
Type Conference
Year 2006
Where ANTS
Authors Guénaël Renault, Kazuhiro Yokoyama
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