Conquering Inseparability: Primary Decomposition and Multivariate Factorization over Algebraic Function Fields of Small Characteristic
Allan Steel, University of Sydney
Algebraic function fields in small characteristic are non-perfect fields, and the standard algorithms to solve some fundamental problems for polynomials simply do not work over these fields. These problems include computing primary decompositions and radicals of ideals over such fields, and factorization of polynomials. I will present a new unified approach which solves these problems in practice for the first time. All of the algorithms have been implemented in the Magma Computer Algebra system, and several examples will demonstrate how the algorithms work.