Details of talk
|Title||Computations with Galois groups|
|Presenter||Nicole Sutherland (The University of Sydney)|
|Session||Algebra and Discrete Mathematics|
Algorithms to compute Galois groups of irreducible polynomials over the rational field have been available in some way for some time. These algorithms have been extended to polynomials of larger degrees and also polynomials over other coefficient rings. Currently the widest ranging algorithm is that of Fieker and Kl\"uners which has no degree restriction on input polynomials and has been adapted for use with reducible as well as irreducible polynomials over algebraic number fields, rational function fields of all characteristics and global algebraic function fields. In this talk I will briefly summarise this algorithm and discuss how we can do further computations with Galois groups using the information we have from the initial computation.