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Magma supports finite extensions of the ring Zp of p-adic integers or
the field Qp of p-adic numbers. Within this chapter, we mean these
objects if we refer to local rings or fields. Section Background
provides more background information on the theory behind the p-adics.
Magma has three different models for working with these locals: fixed precision
rings (RngPadRes and RngPadResExt, with element types
RngPadResElt and RngPadResExtElt), free precision rings
(RngPad and FldPad, with element types RngPadElt
and FldPadElt) and exact p-adic rings (RngXPad and FldXPad with element types RngXPadElt and FldXPadElt).
The merits of each model are discussed in Section p-adic Rings.
Magma also contains a type of local field where extensions can be made by any
irreducible polynomial. For more information on these local fields, see
Chapter GENERAL p-ADIC EXTENSIONS.
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