Computing splitting fields using Galois theory and other Galois constructions

We describe algorithms to compute splitting fields and towers of radical extensions in which a polynomial splits, without us-ing 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 computa-tion of geometric Galois groups (monodromy groups) and their use in computing absolute factorizations.(c) 2022 Elsevier Ltd. All rights reserved.