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.
Liste complète des métadonnées

Cited literature [20 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01337040
Contributor : Lip6 Publications <>
Submitted on : Wednesday, November 23, 2016 - 4:46:46 PM
Last modification on : Thursday, March 21, 2019 - 1:20:53 PM
Document(s) archivé(s) le : Monday, March 20, 2017 - 11:50:50 PM

File

final_RenaultYokoyama_3.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01337040, version 1

Citation

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⟩

Share

Metrics

Record views

147

Files downloads

118