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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 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.
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