ISBN:  Unavailable

Category: Unavailable

Page count: 9

Abstract: "In 1985 Lenstra and van der Hulst [2] demonstrated that sufficiently strong explicit measures of algebraic independence can be used to provide fast factorization of multivariate integer polynomials. Motivated by their result, we adapt an old approach of Mahler [6] to provide the first explicit measure of algebraic independence for e[superscript [alpha]1] ..., e[superscript [alpha][subscript m], where [alpha]1 ..., [alpha][subscript m] are algebraic numbers linearly independent over the rationals. We also show that, because of the amount of precision required, these explicit measures of algebraic independence are not strong enough, even in the most promising cases, to produce fast factorizations of multivariate integer polynomials."