Modular Las Vegas algorithms for polynomial absolute factorization

Let f(X, Y ) ∈ Z[X, Y ] be an irreducible polynomial over Q. We give a Las Vegas absolute irreducibility test based on a property of the Newton polytope of f, or more precisely, of f modulosomeprimeintegerp.Thesameideaofchoosingap satisfyingsomeprescribedproperties together with LLL is used to provide a new strategy for absolute factorization of f(X, Y ). We present our approach in the bivariate case but the techniques extend to the multivariate case. Maple computations show that it is ecient and promising as we are able to construct the algebraic extension containing one absolute factor of a polynomial of degree up to 400. Key words: Absolute factorization, modular computations, LLL algorithm, Newton polytope.

• Type: Journal
• Year: 2010
• Where: JSC
• Authors: Cristina Bertone, Guillaume Chèze, André Galligo
• Keywords: Absolute Factorization, Irreducible Polynomial, JSC 2010, Vegas Absolute Irreducibility