Local trivia (#1220)

* add attributes so some fields

* "fix" precision settings

solves Tommy's log problem
Underlying problem:
  map_coefficients is clever: a zero coefficient is mapped
  to zero(target), thus when applying it with
    x->setprecision(x, new)
  the target precision is ignored and the ring precision is used
  instead

src/LocalField/Elem.jl

@@ -693,7 +693,9 @@ function Base.:(^)(a::LocalFieldElem, n::Int)
   e = absolute_ramification_index(parent(a))
   v = valuation(n, prime(parent(a)))
   if v > 0
-    b = setprecision(a.data, precision(a.data)+v)
+    b = setprecision(base_ring(a.data), precision(a.data)+v) do
+            setprecision(a.data, precision(a.data)+v)
+        end
   else
     b = a.data
   end

src/LocalField/Types.jl

@@ -3,7 +3,7 @@ abstract type EisensteinLocalField <: LocalFieldParameter end
 abstract type UnramifiedLocalField <: LocalFieldParameter end
 abstract type GenericLocalField <: LocalFieldParameter end
 
-mutable struct LocalField{S, T} <: NonArchLocalField
+@attributes mutable struct LocalField{S, T} <: NonArchLocalField
   def_poly::Function #Int -> Poly at prec n
   def_poly_cache::Dict{Int, Generic.Poly{S}}
   S::Symbol

test/LocalField/LocalField.jl

@@ -286,4 +286,15 @@
     n, x = Hecke.image_of_logarithm_one_units(Qp)
     @test n == 1 && length(x) == 1
   end
+
+  @testset "log problems" begin
+    Qx, x = QQ["x"]
+    f = x^4 - 52*x^2 + 26
+    K, a = number_field(f; cached = false)
+    u = 1//5*a^2 - 51//5
+    OK = maximal_order(K)
+    P = prime_decomposition(OK, 2)[1][1]
+    C, mC = completion(K, P)
+    @test valuation(log(mC(u))) == 1//2
+  end
 end