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PadicFieldFamily -- class for p-adic fields

Description

For any prime $p$, the $p$-adic field $\QQ_p$ is represented in Macaulay2 by the object QQ_p.

i1 : QQ_7

o1 = QQ
       7

o1 : PadicFieldFamily
 
i2 : class QQ_7

o2 = PadicFieldFamily

o2 : Type

Elements of $\QQ_p$ are created by applying the field to a number. The default precision is 20 base-$p$ digits; an explicit precision $N$ may be supplied as a first argument.

i3 : QQ_7 3

o3 = 3

o3 : QQ  (of precision 20)
       7
 
i4 : QQ_7(30, 3)

o4 = 3

o4 : QQ  (of precision 30)
       7

Menu

Methods that use a p-adic field family:

  • Number ^ PadicFieldFamily -- see lift(PadicNumber,type of ZZ) -- lift a p-adic number to another ring
  • PadicFieldFamily Thing (missing documentation)
  • padicValuation(PadicFieldFamily) (missing documentation)
  • prime(PadicFieldFamily) -- see prime -- prime of a p-adic field or number
  • Number _ PadicFieldFamily -- see promote(ZZ,type of PadicNumber) -- promote a number to a p-adic field
  • valuation(PadicFieldFamily) (missing documentation)

For the programmer

The object PadicFieldFamily is a type, with ancestor classes RingFamily < Type < MutableHashTable < HashTable < Thing.

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/Padic.m2:462:0.