2008
Multi-modular algorithm for computing the splitting field of a polynomial
Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC
- ,
- 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
- ID information
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- DOI : 10.1145/1390768.1390803
- SCOPUS ID : 57649100551