@inproceedings{37d302a4118a4f0b8ece4a0261078c15,
title = "Multi-modular algorithm for computing the splitting field of a polynomial",
abstract = "Let f be a univariate monic integral polynomial of degree n and let (α1...,αn) be an n-tuple of its roots in an algebraic closure {\=ℚ} of ℚ. Obtaining an algebraic representation of the splitting field ℚ (α1...,αn) of f is a question of first importance in effective Galois theory. For instance, it allows us to manipulate symbolically the roots of f. In this paper, we propose a new method based on multi-modular strategy. Actually, we provide algorithms for this task which return a triangular set encoding the splitting ideal of f. We examine the ability/practicality of the method by experiments on a real computer and study its complexity.",
keywords = "Galois theory, Splitting field",
author = "Gu{\'e}na{\"e}l Renault and Kazuhiro Yokoyama",
year = "2008",
month = dec,
day = "18",
doi = "10.1145/1390768.1390803",
language = "English",
isbn = "9781595939043",
series = "Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC",
pages = "247--254",
booktitle = "ISSAC'08",
note = "21st Annual Meeting of the International Symposium on Symbolic Computation, ISSAC 2008 ; Conference date: 20-07-2008 Through 23-07-2008",
}