Algorithms for enumerating invariants and extensions of local fields

There are many computationally difficult problems in the study of p-adic fields, among them the classification of field extensions and the decomposition of global ideals. The main goal of this work is present efficient algorithms, leveraging the Newton polygons and residual polynomials, to solve many of these problems faster and more efficiently than present methods. Considering additional invariants, we extend Krasner's mass formula, dramatically improve general extension enumeration using the reduced Eisenstein polynomials of Monge, and provide a detailed account of algorithms that compute Okutsu invariants, which have many uses, through the lens of partitioning the set of zeros of polynomials