Example in Qadic

[gvanuxem]

julia> using Nemo

Welcome to Nemo version 0.49.3

Nemo comes with absolutely no warranty whatsoever

julia> R, _ = qadic_field(7, 1, precision = 30);

julia> a = 1 + 2*7 + 4*7^2 + O(R, 7^3)
7^0 + 2*7^1 + 4*7^2 + O(7^3)

julia> b = 7^2 + 3*7^3 + O(R, 7^5)
7^2 + 3*7^3 + O(7^5)

julia> c = R(2)
2*7^0 + O(7^30)

julia> k = precision(a)
3

julia> m = prime(R)
7

julia> n = valuation(b)
2

julia> Qx, x = QQ["x"]
(Univariate polynomial ring in x over QQ, x)

julia> p = lift(Qx, a)
211

julia> Zy, y = ZZ["y"]
(Univariate polynomial ring in y over ZZ, y)

julia> q = lift(Zy, divexact(a, b))
ERROR: Unable to lift
Stacktrace:
 [1] error(s::String)
   @ Base ./error.jl:35
 [2] lift(R::ZZPolyRing, a::QadicFieldElem)
   @ Nemo ~/.julia/packages/Nemo/4IPsx/src/flint/qadic.jl:170
 [3] top-level scope
   @ REPL[12]:1

julia>

[joschmitt]

The quotient has valuation -2, how should this lift to the integers?

julia> R, _ = qadic_field(7, 1, precision = 30);

julia> a = 1 + 2*7 + 4*7^2 + O(R, 7^3)
7^0 + 2*7^1 + 4*7^2 + O(7^3)

julia> b = 7^2 + 3*7^3 + O(R, 7^5)
7^2 + 3*7^3 + O(7^5)

julia> valuation(divexact(a, b))
-2

julia> lift(Qx, divexact(a, b))
337//49