feat: try to make padic regulator faster

examples/NFDB.jl

@@ -1156,7 +1156,7 @@ end
 #
 ################################################################################
 
-function _p_adic_regulator(K, p)
+function _p_adic_regulator(K, p, fast::Bool = false)
   if !is_normal(K)
     return _padic_regulator_non_normal(K, p)
   end
@@ -1173,9 +1173,18 @@ function _p_adic_regulator(K, p)
     if prec > 2^15
       error("Precision >= 2^15, something is wrong")
     end
-    C, mC = completion(K, P, prec)
+    local C, mC
+    if fast
+      try
+        C, mC = completion_easy(K, P)
+      catch
+        C, mC = completion(K, P)
+      end
+    else
+      C, mC = completion(K, P)
+    end
     Rmat = zero_matrix(C, r, r)
-    D = Dict{nf_elem, LocalFieldElem{qadic, EisensteinLocalField}}()
+    D = Dict{nf_elem, elem_type(C)}()
     for i in 1:r
       for j in 1:r
         Rmat[i, j] = _evaluate_log_of_fac_elem(mC, P, mA(A[i])(mU(U[j + 1])), D) # j + 1, because the fundamental units correspond to U[2],..,U[r + 1]

src/LocalField/Conjugates.jl

@@ -372,7 +372,7 @@ function regulator_iwasawa(u::Vector{T}, C::qAdicConj, n::Int = 10) where {T<: U
   @assert is_totally_real(k)
   c = map(x -> conjugates_log(x, C, n, all = true, flat = false), u)
   m = matrix(c)
-  m = hcat(m, matrix(base_ring(m), nrows(m), 1, [one(base_ring(m)) for i=1:nrows(m)]))
+  m = vcat(m, matrix(base_ring(m), 1, ncols(m), [one(base_ring(m)) for i=1:ncols(m)]))
   return det(m)//degree(k)
 end