thofma · lgoettgens · Jan 18, 2024 · Jan 23, 2024
diff --git a/examples/IsPower.jl b/examples/IsPower.jl
@@ -209,7 +209,7 @@ function Base.lastindex(M::MatElem, i::Int)
   error("illegal dimensino")
 end
 
-function Hecke.is_power(a::qadic, i::Int)
+function Hecke.is_power(a::QadicFieldElem, i::Int)
   @assert i>0
   if i==1
     return true, a
@@ -238,7 +238,7 @@ function Hecke.is_power(a::qadic, i::Int)
   return true, b*uniformizer(parent(a))^rv
 end
 
-function Hecke.roots(a::qadic, i::Int)
+function Hecke.roots(a::QadicFieldElem, i::Int)
   @assert i>0
   if i==1
     return a
@@ -373,11 +373,11 @@ function Hecke.crt(v::Vector{ZZPolyRingElem}, m::Vector{ZZPolyRingElem}, H::Heck
   return res[end]
 end
 
-function Hecke.degree(R::qadic) #TODO XXXX
+function Hecke.degree(R::QadicFieldElem) #TODO XXXX
   return R.length
 end
 
-function Hecke.ideal(R::NfAbsOrd, f::MapFromFunc{AnticNumberField,FlintQadicField})
+function Hecke.ideal(R::NfAbsOrd, f::MapFromFunc{AnticNumberField,QadicField})
   K = nf(R)
   Cq = codomain(f)
   if degree(Cq) == degree(K)

diff --git a/examples/MultDep.jl b/examples/MultDep.jl
@@ -346,7 +346,7 @@ function verify_gamma(a::Vector{FacElem{nf_elem, AnticNumberField}}, g::Vector{Z
   return B > sum(x*x for x = b)
 end
 
-function lift_reco(::QQField, a::padic; reco::Bool = false)
+function lift_reco(::QQField, a::PadicFieldElem; reco::Bool = false)
   if reco
     u, v, N = getUnit(a)
     R = parent(a)

diff --git a/src/Deprecations.jl b/src/Deprecations.jl
@@ -28,9 +28,9 @@
 
 @deprecate automorphisms(x::NumField) automorphism_list(x)
 
-@deprecate automorphisms(x::Union{FlintPadicField, FlintQadicField, LocalField}) automorphism_list(x)
+@deprecate automorphisms(x::Union{PadicField, QadicField, LocalField}) automorphism_list(x)
 
-@deprecate automorphisms(x::LocalField, y::Union{FlintPadicField, FlintQadicField, LocalField}) automorphism_list(x, y)
+@deprecate automorphisms(x::LocalField, y::Union{PadicField, QadicField, LocalField}) automorphism_list(x, y)
 
 # Deprecated during 0.18.*
 
@@ -107,7 +107,7 @@
 
 @deprecate roots(f::Union{ZZPolyRingElem, QQPolyRingElem}, R::AcbField, abs_tol::Int=R.prec, initial_prec::Int...) roots(R, f, abs_tol, initial_prec...)
 
-@deprecate roots(f::ZZPolyRingElem, Q::FlintQadicField; max_roots::Int = degree(f)) roots(Q, f; max_roots = max_roots)
+@deprecate roots(f::ZZPolyRingElem, Q::QadicField; max_roots::Int = degree(f)) roots(Q, f; max_roots = max_roots)
 
 @deprecate roots(f::ZZPolyRingElem, Q::QQField; max_roots::Int = degree(f)) roots(Q, f; max_roots = max_roots)
 

diff --git a/src/HeckeTypes.jl b/src/HeckeTypes.jl
@@ -2226,9 +2226,9 @@ mutable struct qAdicRootCtx
   f::ZZPolyRingElem
   p::Int
   n::Int
-  Q::Vector{FlintQadicField}
+  Q::Vector{QadicField}
   H::Hecke.HenselCtx
-  R::Vector{qadic}
+  R::Vector{QadicFieldElem}
   is_splitting::Bool
   function qAdicRootCtx(f::ZZPolyRingElem, p::Int; splitting_field::Bool = false)
     r = new()

diff --git a/src/LocalField/Completions.jl b/src/LocalField/Completions.jl
@@ -19,7 +19,7 @@ function image(f::CompletionMap, a::nf_elem)
   return z
 end
 
-function preimage(f::CompletionMap{LocalField{qadic, EisensteinLocalField}, LocalFieldElem{qadic, EisensteinLocalField}}, a::LocalFieldElem{qadic, EisensteinLocalField})
+function preimage(f::CompletionMap{LocalField{QadicFieldElem, EisensteinLocalField}, LocalFieldElem{QadicFieldElem, EisensteinLocalField}}, a::LocalFieldElem{QadicFieldElem, EisensteinLocalField})
   Kp = codomain(f)
   @assert Kp === parent(a)
   Qq = base_field(Kp)
@@ -43,12 +43,12 @@ function preimage(f::CompletionMap{LocalField{qadic, EisensteinLocalField}, Loca
   return evaluate(r, f.inv_img[2])
 end
 
-function preimage(f::CompletionMap{LocalField{padic, EisensteinLocalField}, LocalFieldElem{padic, EisensteinLocalField}}, a::LocalFieldElem{padic, EisensteinLocalField})
+function preimage(f::CompletionMap{LocalField{PadicFieldElem, EisensteinLocalField}, LocalFieldElem{PadicFieldElem, EisensteinLocalField}}, a::LocalFieldElem{PadicFieldElem, EisensteinLocalField})
   @assert codomain(f) === parent(a)
   return evaluate(map_coefficients(lift, a.data), f.inv_img[2])
 end
 
-function preimage(f::CompletionMap{FlintQadicField, qadic}, a::qadic)
+function preimage(f::CompletionMap{QadicField, QadicFieldElem}, a::QadicFieldElem)
   Kp = codomain(f)
   @assert Kp == parent(a)
   Qpx = parent(defining_polynomial(Kp))
@@ -170,7 +170,7 @@ function completion(K::AnticNumberField, P::NfOrdIdl, precision::Int = 64)
   pol_gen = Qqx(coeffs_eisenstein)
   Kp, gKp = eisenstein_extension(pol_gen, "a", cached = false)
   Kp.def_poly = x->setprecision(pol_gen, x)
-  img_prim_elem = Vector{qadic}(undef, e)
+  img_prim_elem = Vector{QadicFieldElem}(undef, e)
   for i = 1:e
     coeff = Qq()
     for j = 0:f-1
@@ -241,7 +241,7 @@ else
   fl, xZp = can_solve_with_solution(MZp, bZp, side = :left)
   @assert fl
 end 
-  coeffs_eisenstein = Vector{qadic}(undef, e+1)
+  coeffs_eisenstein = Vector{QadicFieldElem}(undef, e+1)
   gQq = gen(Qq)
   for i = 1:e
     coeff = zero(Qq)
@@ -259,7 +259,7 @@ end
 
 
 
-function setprecision!(f::CompletionMap{LocalField{qadic, EisensteinLocalField}, LocalFieldElem{qadic, EisensteinLocalField}}, new_prec::Int)
+function setprecision!(f::CompletionMap{LocalField{QadicFieldElem, EisensteinLocalField}, LocalFieldElem{QadicFieldElem, EisensteinLocalField}}, new_prec::Int)
   P = prime(f)
   OK = order(P)
   new_prec += valuation(denominator(basis_matrix(OK, copy = false)), P)
@@ -296,7 +296,7 @@ function setprecision!(f::CompletionMap{LocalField{qadic, EisensteinLocalField},
 
     pol_gen = Qqx(coeffs_eisenstein)
     Kp.def_poly_cache[new_prec] = pol_gen
-    img_prim_elem = Vector{qadic}(undef, e)
+    img_prim_elem = Vector{QadicFieldElem}(undef, e)
     for i = 1:e
       coeff = Qq()
       for j = 0:_f-1
@@ -351,14 +351,14 @@ function totally_ramified_completion(K::AnticNumberField, P::NfOrdIdl, precision
   bZp = map_entries(Zp, bK.num)
   fl, xZp = can_solve_with_solution(MZp, bZp, side = :left)
   @assert fl
-  coeffs_eisenstein = Vector{padic}(undef, e+1)
+  coeffs_eisenstein = Vector{PadicFieldElem}(undef, e+1)
   for i = 1:e
     coeffs_eisenstein[i] = -xZp[1, i].x
   end
   coeffs_eisenstein[e+1] = one(Qp)
   pol_gen = Qpx(coeffs_eisenstein)
   Kp, gKp = eisenstein_extension(pol_gen, "a")
-  img_prim_elem = Vector{padic}(undef, e)
+  img_prim_elem = Vector{PadicFieldElem}(undef, e)
   for i = 1:e
     img_prim_elem[i] = xZp[2, i].x
   end
@@ -372,7 +372,7 @@ function totally_ramified_completion(K::AnticNumberField, P::NfOrdIdl, precision
 end
 
 
-function setprecision!(f::CompletionMap{LocalField{padic, EisensteinLocalField}, LocalFieldElem{padic, EisensteinLocalField}}, new_prec::Int)
+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)
@@ -400,7 +400,7 @@ function setprecision!(f::CompletionMap{LocalField{padic, EisensteinLocalField},
     bQp = map_entries(Zp, bK)
     fl, xZp = can_solve_with_solution(MZp, bZp, side = :left)
     @assert fl
-    coeffs_eisenstein = Vector{padic}(undef, e+1)
+    coeffs_eisenstein = Vector{PadicFieldElem}(undef, e+1)
     for i = 1:e
       coeffs_eisenstein[i] = -xZp[1, i].x
     end
@@ -409,7 +409,7 @@ function setprecision!(f::CompletionMap{LocalField{padic, EisensteinLocalField},
     Kp.def_poly_cache[new_prec] = pol_gen
     Kp.precision = new_prec
     #Should I update the traces too?
-    img_prim_elem = Vector{padic}(undef, e)
+    img_prim_elem = Vector{PadicFieldElem}(undef, e)
     for i = 1:e
       img_prim_elem[i] = xZp[2, i].x
     end
@@ -483,7 +483,7 @@ function unramified_completion(K::AnticNumberField, P::NfOrdIdl, precision::Int
   return Qq, completion_map
 end
 
-function setprecision!(f::CompletionMap{FlintQadicField, qadic}, new_prec::Int)
+function setprecision!(f::CompletionMap{QadicField, QadicFieldElem}, new_prec::Int)
   Kp = codomain(f)
   setprecision!(Kp, new_prec)
   if new_prec < f.precision

diff --git a/src/LocalField/Conjugates.jl b/src/LocalField/Conjugates.jl
@@ -1,5 +1,5 @@
 #XXX: valuation(Q(0)) == 0 !!!!!
-function newton_lift(f::ZZPolyRingElem, r::qadic, prec::Int = parent(r).prec_max, starting_prec::Int = 2)
+function newton_lift(f::ZZPolyRingElem, r::QadicFieldElem, prec::Int = parent(r).prec_max, starting_prec::Int = 2)
   Q = parent(r)
   n = prec
   i = n
@@ -67,14 +67,14 @@ function newton_lift(f::ZZPolyRingElem, r::LocalFieldElem, precision::Int = pare
 end
 
 @doc raw"""
-    roots(Q::FlintQadicField, f::ZZPolyRingElem; max_roots::Int = degree(f)) -> Vector{qadic}
+    roots(Q::QadicField, f::ZZPolyRingElem; max_roots::Int = degree(f)) -> Vector{QadicFieldElem}
 
 The roots of $f$ in $Q$, $f$ has to be square-free (at least the roots have to be simple roots).
 """
-function roots(Q::FlintQadicField, f::ZZPolyRingElem; max_roots::Int = degree(f))
+function roots(Q::QadicField, f::ZZPolyRingElem; max_roots::Int = degree(f))
   k, mk = residue_field(Q)
   rt = roots(k, f)
-  RT = qadic[]
+  RT = QadicFieldElem[]
   for r = rt
     push!(RT, newton_lift(f, preimage(mk, r)))
     if length(RT) >= max_roots
@@ -91,7 +91,7 @@ function roots(C::qAdicRootCtx, n::Int = 10)
     return [setprecision(x, n) for x = C.R]
   end
   lf = factor_mod_pk(Array, C.H, n)
-  rt = qadic[]
+  rt = QadicFieldElem[]
   for Q = C.Q
     Q.prec_max = n
     for x = lf
@@ -101,7 +101,7 @@ function roots(C::qAdicRootCtx, n::Int = 10)
     end
   end
   if isdefined(C, :R)
-    st = qadic[]
+    st = QadicFieldElem[]
     for r = C.R
       p = findfirst(x -> degree(parent(r)) == degree(parent(x)) && iszero(x-r), rt)
       push!(st, rt[p])
@@ -182,8 +182,8 @@ function conjugates(a::nf_elem, C::qAdicConj, n::Int = 10; flat::Bool = false, a
   end
 end
 
-function expand(a::Vector{qadic}; all::Bool, flat::Bool, degs::Vector{Int}= Int[])
-  re = qadic[]
+function expand(a::Vector{QadicFieldElem}; all::Bool, flat::Bool, degs::Vector{Int}= Int[])
+  re = QadicFieldElem[]
   if all
     for ix = 1:length(a)
       x = a[ix]
@@ -206,7 +206,7 @@ function expand(a::Vector{qadic}; all::Bool, flat::Bool, degs::Vector{Int}= Int[
     re = a
   end
   if flat
-    r = padic[]
+    r = PadicFieldElem[]
     for x = re
       for i=1:degree(parent(x))
         push!(r, coeff(x, i-1))
@@ -225,15 +225,15 @@ function _conjugates(a::nf_elem, C::qAdicConj, n::Int, op::Function)
   Zx = polynomial_ring(FlintZZ, cached = false)[1]
   d = denominator(a)
   f = Zx(d*a)
-  res = qadic[]
+  res = QadicFieldElem[]
   for x = R
-    a = op(inv(parent(x)(d))*f(x))::qadic
+    a = op(inv(parent(x)(d))*f(x))::QadicFieldElem
     push!(res, a)
   end
   return res
 end
 
-function _log(a::qadic)
+function _log(a::QadicFieldElem)
   q = prime(parent(a))^degree(parent(a))
   if iseven(q) # an error in flint
     return log((a^(q-1))^2)//2//(q-1)
@@ -268,7 +268,7 @@ end
 
 function conjugates_log(a::FacElem{nf_elem, AnticNumberField}, C::qAdicConj, n::Int = 10; all::Bool = false, flat::Bool = true)
   first = true
-  local res::Vector{qadic}
+  local res::Vector{QadicFieldElem}
   for (k, v) = a.fac
     try
       y = conjugates_log(k, C, n, flat = false, all = false)
@@ -306,10 +306,10 @@ function conjugates_log(a::FacElem{nf_elem, AnticNumberField}, C::qAdicConj, n::
 end
 
 
-function special_gram(m::Vector{Vector{qadic}})
-  g = Vector{padic}[]
+function special_gram(m::Vector{Vector{QadicFieldElem}})
+  g = Vector{PadicFieldElem}[]
   for i = m
-    r = padic[]
+    r = PadicFieldElem[]
     for j = m
       k = 1
       S = 0
@@ -329,7 +329,7 @@ function special_gram(m::Vector{Vector{qadic}})
   return g
 end
 
-function special_gram(m::Vector{Vector{padic}})
+function special_gram(m::Vector{Vector{PadicFieldElem}})
   n = transpose(matrix(m))
   n = transpose(n)*n
   return [[n[i,j] for j=1:ncols(n)] for i = 1:nrows(n)]
@@ -360,9 +360,9 @@ function regulator(R::NfAbsOrd{AnticNumberField, nf_elem}, C::qAdicConj, n::Int
 end
 
 @doc raw"""
-    regulator_iwasawa(u::Vector{T}, C::qAdicConj, n::Int = 10) where {T<: Union{nf_elem, FacElem{nf_elem, AnticNumberField}}} -> qadic
-    regulator_iwasawa(K::AnticNumberField, C::qAdicConj, n::Int = 10) -> qadic
-    regulator_iwasawa(R::NfAbsOrd, C::qAdicConj, n::Int = 10) -> qadic
+    regulator_iwasawa(u::Vector{T}, C::qAdicConj, n::Int = 10) where {T<: Union{nf_elem, FacElem{nf_elem, AnticNumberField}}} -> QadicFieldElem
+    regulator_iwasawa(K::AnticNumberField, C::qAdicConj, n::Int = 10) -> QadicFieldElem
+    regulator_iwasawa(R::NfAbsOrd, C::qAdicConj, n::Int = 10) -> QadicFieldElem
 
 For a totally real field $K$, the regulator as defined by Iwasawa: the determinant of the
 matrix containing the logarithms of the conjugates, supplemented by a column containing all $1$.
@@ -497,7 +497,7 @@ end
 
 @doc raw"""
     completion_easy(K::AnticNumberField, P::NfOrdIdl)
-                                               -> FlintQadicField, CompletionMap
+                                               -> QadicField, CompletionMap
 
 The completion of $K$ wrt to the topology induced by the valuation at the
 unramified prime ideal $P$.
@@ -519,7 +519,7 @@ end
 completion(K::AnticNumberField, p::Integer, i::Int, precision::Int = 64) = completion(K, ZZRingElem(p), i, precision)
 
 @doc raw"""
-    completion(K::AnticNumberField, p::ZZRingElem, i::Int) -> FlintQadicField, Map
+    completion(K::AnticNumberField, p::ZZRingElem, i::Int) -> QadicField, Map
 
 The completion corresponding to the $i$-th conjugate in the non-canonical ordering of
 `conjugates`.
@@ -532,7 +532,7 @@ function completion(K::AnticNumberField, p::ZZRingElem, i::Int, n = 64)
   return completion(K, ca)
 end
 
-function completion(K::AnticNumberField, ca::qadic)
+function completion(K::AnticNumberField, ca::QadicFieldElem)
   p = prime(parent(ca))
   C = qAdicConj(K, Int(p))
   r = roots(C.C, precision(ca))
@@ -585,7 +585,7 @@ function completion(K::AnticNumberField, ca::qadic)
 
   c = lift_root(f, a, b, p, 10)
   pc = ZZRingElem(10)
-  function lif(x::qadic)
+  function lif(x::QadicFieldElem)
     if iszero(x)
       return K(0)
     end