Fix 1509 (thofma#1511)

src/LocalField/Completions.jl

@@ -10,7 +10,7 @@ function image(f::CompletionMap, a::AbsSimpleNumFieldElem)
   end
   Qx = parent(parent(a).pol)
   z = evaluate(Qx(a), f.prim_img)
-  if !is_unit(z) 
+  if !is_unit(z)
     v = valuation(a, f.P)
     a = a*uniformizer(f.P).elem_in_nf^-v
     z = evaluate(Qx(a), f.prim_img)
@@ -27,7 +27,7 @@ function preimage(f::CompletionMap{LocalField{QadicFieldElem, EisensteinLocalFie
   coeffs = Vector{AbsSimpleNumFieldElem}()
   #careful: we're working in a limited precision world and the lift
   #can be waaaay to large
-  if abs(valuation(a)) > 100
+  if !iszero(a) && abs(valuation(a)) > 100
     global last_a = a
     error("elem too large")
   end
@@ -131,7 +131,7 @@ The map giving the embedding of $K$ into the completion, admits a pointwise
 preimage to obtain a lift. Note, that the map is not well defined by this
 data: $K$ will have $\deg P$ many embeddings.
 
-The map is guaranteed to yield a relative precision of at least `preciscion`. 
+The map is guaranteed to yield a relative precision of at least `preciscion`.
 """
 function completion(K::AbsSimpleNumField, P::AbsNumFieldOrderIdeal{AbsSimpleNumField, AbsSimpleNumFieldElem}, precision::Int = 64)
   #to guarantee a rel_prec we need to account for the index (or the
@@ -179,7 +179,7 @@ function completion(K::AbsSimpleNumField, P::AbsNumFieldOrderIdeal{AbsSimpleNumF
     img_prim_elem[i] = coeff
   end
   img = Kp(Qqx(img_prim_elem))
-  
+
   u = uniformizer(P).elem_in_nf
   completion_map = CompletionMap(K, Kp, img, (gq_in_K, u), precision)
   completion_map.P = P
@@ -193,7 +193,7 @@ function _solve_internal(gq_in_K, P, precision, Zp, Qq)
   precision += e - (precision % e)
   @assert precision % e == 0
   #problem/ feature:
-  #the lin. alg is done in/over Zp or Qp, thus precision is measured in 
+  #the lin. alg is done in/over Zp or Qp, thus precision is measured in
   #block of length e (power of the prime number p, rather than powers of
   #pi, the prime element)
   #so it is a good idea to increase the precision to be divisible by e
@@ -231,7 +231,7 @@ if true
   # the can_solve... returns a precision of just 6 p-adic digits
   # the snf gets 16 (both for the default precision)
   # the det(M) has valuation 12, but the elem. divisors only 3
-  #TODO: rewrite can_solve? look at Avi's stuff? 
+  #TODO: rewrite can_solve? look at Avi's stuff?
   # x M = b
   # u*M*v = s
   # x inv(u) u M v = b v
@@ -251,7 +251,7 @@ else
   bZp = map_entries(Zp, bK.num)
   fl, xZp = can_solve_with_solution(MZp, bZp, side = :left)
   @assert fl
-end 
+end
   coeffs_eisenstein = Vector{QadicFieldElem}(undef, e+1)
   gQq = gen(Qq)
   for i = 1:e
@@ -276,7 +276,7 @@ function setprecision!(f::CompletionMap{LocalField{QadicFieldElem, EisensteinLoc
   new_prec += valuation(denominator(basis_matrix(OK, copy = false)), P)
 
   if new_prec < f.precision
-    K = domain(f)
+    K = codomain(f)
     setprecision!(K, new_prec)
     e = ramification_index(P)
     setprecision!(base_field(K), div(new_prec+e-1, e))
@@ -296,7 +296,7 @@ function setprecision!(f::CompletionMap{LocalField{QadicFieldElem, EisensteinLoc
 
     Zp = maximal_order(prime_field(Kp))
     Qq = base_field(Kp)
-    
+
     setprecision!(Qq, ex)
     setprecision!(Zp, ex)
     gQq = gen(Qq)
@@ -385,11 +385,12 @@ end
 
 function setprecision!(f::CompletionMap{LocalField{PadicFieldElem, EisensteinLocalField}, LocalFieldElem{PadicFieldElem, EisensteinLocalField}}, new_prec::Int)
   if new_prec < f.precision
-    K = domain(f)
-    setprecision!(K, new_prec)
-    setprecision!(base_field(K), new_prec)
+    Kp = codomain(f)
+    setprecision!(Kp, new_prec)
+    setprecision!(base_field(Kp), new_prec)
     setprecision!(f.prim_img, new_prec)
   else
+    K = domain(f)
     #I need to increase the precision of the data
     P = prime(f)
     e = ramification_index(P)
@@ -402,13 +403,13 @@ function setprecision!(f::CompletionMap{LocalField{PadicFieldElem, EisensteinLoc
     end
     Qp = PadicField(prime(Kp), div(new_prec, e)+1)
     Zp = maximal_order(Qp)
-    Qpx = polynomial_ring(Qp, "x")
+    Qpx, _ = polynomial_ring(Qp, "x")
     pows_u = powers(u, e-1)
     bK = basis_matrix(AbsSimpleNumFieldElem[u*pows_u[end], gen(K)])
     append!(pows_u, map(elem_in_nf, basis(P^new_prec, copy = false)))
     MK = basis_matrix(pows_u)
-    MQp = map_entries(Zp, MK)
-    bQp = map_entries(Zp, bK)
+    MZp = map_entries(Zp, MK)
+    bZp = map_entries(Zp, bK)
     fl, xZp = can_solve_with_solution(MZp, bZp, side = :left)
     @assert fl
     coeffs_eisenstein = Vector{PadicFieldElem}(undef, e+1)
@@ -501,14 +502,13 @@ function setprecision!(f::CompletionMap{QadicField, QadicFieldElem}, new_prec::I
     setprecision!(f.prim_img, new_prec)
   else
     P = prime(f)
-    f = inertia_degree(P)
     gq, u = f.inv_img
     Zx = polynomial_ring(FlintZZ, "x")[1]
     q, mq = residue_field(Kp)
     pol_gq = lift(Zx, defining_polynomial(q))
     gq = _increase_precision(gq, pol_gq, f.precision, new_prec, P)
-    f.inv_img[1] = gq
-    setprecision!(Qq, new_prec)
+    f.inv_img = (gq, u)
+    setprecision!(Kp, new_prec)
     #To increase the precision of the image of the primitive element, I use Hensel lifting
     f.prim_img = newton_lift(Zx(defining_polynomial(domain(f))), f.prim_img, new_prec, f.precision)
   end

test/LocalField/Completions.jl

@@ -39,6 +39,30 @@ end
   @test precision(bb) >= 20
 end
 
+@testset "Issue 1509" begin
+  F, _ = cyclotomic_field(3)
+  OF = maximal_order(F);
+  K, toK = completion(F, 2*OF);
+  @test iszero(preimage(toK, toK(F(0))))
+  setprecision!(toK, 10)
+  @test precision(toK(F(1))) == 10
+  setprecision!(toK, 70)
+  @test precision(toK(F(1))) == 70
+
+  K, toK = Hecke.unramified_completion(F, 2*OF)
+  setprecision!(toK, 10)
+  @test precision(toK(F(1))) == 10
+  setprecision!(toK, 70)
+  @test precision(toK(F(1))) == 70
+
+  P = prime_decomposition(OF, 7)[1][1]
+  K, toK = Hecke.totally_ramified_completion(F, P)
+  setprecision!(toK, 10)
+  @test precision(toK(F(1))) == 10
+  setprecision!(toK, 70)
+  @test precision(toK(F(1))) == 70
+end
+
 @testset "another issue" begin
   Qx, x = QQ["x"]
   K, a = number_field(Qx([-881539931206823616,457325902411822080,16029750347584272,-124243211029392,-1536813216432,10162275552,33311655,-246753,0,1]), "a", cached = false)
@@ -71,7 +95,7 @@ end
     end
   end
 
-  let 
+  let
     Qx, x = QQ["x"]
     t = [
          (x^2 - 3, 3, 1//2), # C2