Papers

Peer-reviewed
2008

Multi-modular algorithm for computing the splitting field of a polynomial

Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC
  • Guénaël Renault
  • ,
  • Kazuhiro Yokoyama

First page
247
Last page
254
Language
English
Publishing type
Research paper (international conference proceedings)
DOI
10.1145/1390768.1390803
Publisher
ACM

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 ℚ̄ 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.

Link information
DOI
https://doi.org/10.1145/1390768.1390803
ID information
  • DOI : 10.1145/1390768.1390803
  • SCOPUS ID : 57649100551

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