The local fields described in this chapter are extensions of any local field in Magma by any irreducible polynomial over that field. They are not constrained by requirements that the polynomial defining the extension be inertial or eisenstein. These local fields allow for ramified and inertial extensions to be made in one step rather than forcing such an extension to be split into two -- being a ramified extension and an unramified extension. They are typed RngLocA with elements of type RngLocAElt. To compare these fields to the local fields where extensions are either totally ramified or unramified, see Chapter p-ADIC RINGS AND THEIR EXTENSIONS.
The fields are represented as a polynomial quotient ring. A map into an isomorphic FldPad can be constructed and the isomorphic field used for various calculations.
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