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.

• Type: Conference
• Year: 2006
• Where: ANTS
• Authors: Guénaël Renault, Kazuhiro Yokoyama
• Keywords: Algorithms, ANTS 2006, Galois Group Gf, P-adic Stauduhar Method, Splitting Field Kf