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 Gf by p-adic Stauduhar's method. This method uses the knowledge of Gf with its action on the roots of f over a p-adic number field, and it reduces the computation of Kf 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. © Springer-Verlag Berlin Heidelberg 2006.
CITATION STYLE
Renault, G., & Yokoyama, K. (2006). A modular method for computing the splitting field of a polynomial. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4076 LNCS, pp. 124–140). Springer Verlag. https://doi.org/10.1007/11792086_10
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