Conference Papers Year : 2006

A Modular Method for Computing the Splitting Field of a Polynomial

Abstract

We provide a modular method for computing the splitting field $K_f$ of an integral polynomial $f$ by suitable use of the byproduct of computation of its Galois group $G_f$ by $p$-adic Stauduhar’s method. This method uses the knowledge of $G_f$ with its action on the roots of $f$ over a $p$-adic number field, and it reduces the computation of $K_f$ to solving systems of linear equations modulo some powers of $p$ and Hensel liftings. We provide a careful treatment on reducing computational difficulty. We examine the ability/practicality of the method by experiments on a real computer and study its complexity.

Fichier principal
Vignette du fichier
final_RenaultYokoyama_3.pdf (287.7 Ko) Télécharger le fichier
Origin Files produced by the author(s)
Licence
Loading...

Dates and versions

hal-01337040 , version 1 (23-11-2016)

Licence

Identifiers

  • HAL Id : hal-01337040 , version 1

Cite

Guénaël Renault, Kazuhiro Yokoyama. A Modular Method for Computing the Splitting Field of a Polynomial. Algorithmic Number Theory Symposium, Jul 2006, Berlin, Germany. pp.124-140. ⟨hal-01337040⟩
251 View
1113 Download

Share

  • More