Computing splitting fields using Galois theory and other Galois constructions. (May 2023) - Fieker, Claus; Sutherland, Nicole
Abstract: We describe algorithms to compute splitting fields and towers of radical extensions in which a polynomial splits, without using polynomial factorisation in towers or constructing any field properly containing the constructed field, instead extending Galois group computations for this task. We also describe the computation of geometric Galois groups (monodromy groups) and their use in computing absolute factorizations.