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Introduction

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 two different models for working with these locals: fixed precision rings (RngPadRes and RngPadResExt, with element types RngPadResElt and RngPadResExtElt) and free precision rings (RngPad and FldPad, with element types RngPadElt and FldPadElt). 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 LOCAL FIELDS.

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Version: V2.19 of Wed Apr 24 15:09:57 EST 2013