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.