# Introduction

The local fields described in this chapter are extensions of any $p$-adic local field in Magma by any irreducible polynomial over that field. The polynomial defining the extension is not required to be inertial or eisenstein, in contrast to the (older) extensions of $p$-adic fields. This allows 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.

Only fields are implemented in this way – no construction of a ring of integers is provided (although `IntegralBasis` gives a basis for it as a module over the base ring).

These local fields have type `RngLocA` with elements of type `RngLocAElt`, while the local fields described in the previous chapter [$p$-Adic Rings and Their Extensions](../PAdicRingsAndTheirExtensions/index-padic-rings-and-their-extensions.md#rngloc) have type `FldPad`.

These fields (of type `RngLocA`) can be converted to the other representation (type `FldPad`) using `RamifiedRepresentation`, which returns an isomorphism between them. This can be used for calculations not supported for `RngLocA`.