teichmullerLift -- Teichmüller lift of a p-adic integer

Usage:

teichmullerLift x
Inputs:
- x, a p-adic number,
Outputs:
- a p-adic number,

Description

Returns the Teichmüller lift of $x$, which is the unique root of unity $t \in \ZZ_p^\times$ satisfying $t \equiv x \pmod{p}$ and $t^p = t$.

i1 : t = teichmullerLift QQ_7 3

o1 = 3 + 4*7^1 + 6*7^2 + 3*7^3 + 2*7^5 + 6*7^6 + 2*7^7 + 4*7^8 + 3*7^9 +
     4*7^10 + 4*7^11 + 5*7^12 + 2*7^13 + 1*7^14 + 2*7^15 + 1*7^16 + 4*7^17 +
     6*7^18 + 1*7^19

o1 : QQ  (of precision 20)
       7

i2 : t^7 == t

o2 = true

Caveat

An error is raised if $\nu_p(x) < 0$, i.e., if $x$ is not a $p$-adic integer.

Ways to use teichmullerLift:

teichmullerLift(PadicNumber)

For the programmer

The object teichmullerLift is a method function.

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/Padic.m2:989:0.