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Semi-numerical absolute factorization of polynomials with integer coefficients

✍ Scribed by David Rupprecht

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
268 KB
Volume
37
Category
Article
ISSN
0747-7171

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✦ Synopsis

In this paper, we propose a semi-numerical algorithm for computing absolute factorization of multivariate polynomials. It is based on some properties appearing after a generic change of coordinate. Using numerical computation, Galois group action and rational approximation, this method provides an efficient probabilistic algorithm for medium degrees. Two implementations are presented and compared to other algorithms.

πŸ“œ SIMILAR VOLUMES

Factorization of Multivariate Polynomial
Factorization of Multivariate Polynomials with Coefficients in Fp
✍ Guy Viry πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 548 KB

The ring of polynomials in \(X, X_{1}, \ldots, X_{m}\) are denoted by \(\mathbf{F}_{p}\left[X, X_{1}, \ldots, X_{m}\right]\) in \(F_{p}\), that is the field of integers defined modulo \(p\). In the usual factorization algorithm defined by Wang, the given polynomial \(P\) is first factorized modulo \