At the core of any cohomological method in algorithmic number theory is the requirement to work with normal fields, which, by their very nature have a large degree, thus are difficult to work with. In this project we aim to develop techniques that remove the need to explicitly access the normal closure – for select problems. A central tool here is the computation of the Galois group as this allows access to at least some information about the normal closure – without the need to actually compute it.
