2009/11/26 by Cristina Bertone, Bertone, Cristina, Guillaume Chèze +3
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG
paper · pdf · doi:10.48550/arxiv.0911.5024
arxiv created 2010/01/28 · arxiv updated 2010/02/08
Let f(X,Y) ∈ \ZZ[X,Y] be an irreducible polynomial over \QQ. We give a Las Vegas absolute irreducibility test based on a property of the Newton polytope of f, or more precisely, of f modulo some prime integer p. The same idea of choosing a p satisfying some prescribed properties 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 efficient and promising as we are able to factorize some polynomials of degree up to 400.