coefficient_ring -> base_field for the p-adics

examples/NFDB.jl

@@ -1196,7 +1196,7 @@ function _p_adic_regulator_coates(K::AbsSimpleNumField, p::IntegerUnion)
   while true
     (prec > 2^12 || working_prec > 2^12) && error("Something wrong")
     imK =[LocalFieldValuationRingElem{PadicField, PadicFieldElem}[] for i in 1:degK]
-    Qp = PadicField(p, prec, cached = false)
+    Qp = padic_field(p, precision = prec, cached = false)
     Zp = ring_of_integers(Qp)
     dK = discriminant(OK)
     r = maximum([ramification_index(P) for P in dp])

examples/Plesken.jl

@@ -183,7 +183,7 @@ function primitive_root_r_div_qm1(R, r::Int)
 end
 
 function get_f(r::Int, p::ZZRingElem, s::Int)
-  R = PadicField(r, s)
+  R = padic_field(r, precision = s)
   return lift(teichmuller(R(p)))
 end
 # plan

examples/Tropics.jl

@@ -84,7 +84,7 @@ lp[1].gen_two*lp[2].gen_two^2
 ma = representation_matrix(a)
 mb = representation_matrix(k(ans))
 @assert iszero(ma*mb - mb*ma)
-Qp = PadicField(7, 10)
+Qp = padic_field(7, precision = 10)
 Main.TropicalModule.simultaneous_diagonalization([map_entries(Qp, ma), map_entries(Qp, mb)])
 
 =#

src/Deprecations.jl

@@ -273,3 +273,10 @@ end
 # Deprecated in 0.33.0
 
 @deprecate rres reduced_resultant
+
+# Deprecated in 0.34.0
+
+@deprecate lift(a::LocalFieldValuationRingElem) lift(ZZ, a)
+@deprecate prime_field(L::Union{QadicField, LocalField}) absolute_base_field(L)
+@deprecate coefficient_ring(k::LocalField) base_field(k)
+@deprecate coefficient_field(k::QadicField) base_field(k)

src/HeckeTypes.jl

@@ -2240,11 +2240,11 @@ mutable struct qAdicRootCtx
     lf = Hecke.factor_mod_pk(Array, H, 1)
     if splitting_field
       d = lcm([degree(y[1]) for y = lf])
-      R = QadicField(p, d, 1)[1]
+      R = qadic_field(p, d, precision = 1)[1]
       Q = [R]
       r.is_splitting = true
     else
-      Q = [QadicField(p, x, 1)[1] for x = Set(degree(y[1]) for y = lf)]
+      Q = [qadic_field(p, x, precision = 1)[1] for x = Set(degree(y[1]) for y = lf)]
       r.is_splitting = false
     end
     @assert all(x->isone(x[2]), lf)

src/LocalField/Completions.jl

@@ -189,9 +189,9 @@ function completion(K::AbsSimpleNumField, P::AbsNumFieldOrderIdeal{AbsSimpleNumF
   f = degree(P)
   e = ramification_index(P)
   prec_padics = div(precision+e-1, e)
-  Qp = PadicField(minimum(P), prec_padics, cached = false)
+  Qp = padic_field(minimum(P), precision = prec_padics, cached = false)
   Zp = maximal_order(Qp)
-  Qq, gQq = QadicField(minimum(P), f, prec_padics, cached = false)
+  Qq, gQq = qadic_field(minimum(P), f, precision = prec_padics, cached = false)
   Qqx, gQqx = polynomial_ring(Qq, "x")
   q, mq = residue_field(Qq)
   #F, mF = ResidueFieldSmall(OK, P)
@@ -336,7 +336,7 @@ function setprecision!(f::CompletionMap{LocalField{QadicFieldElem, EisensteinLoc
     gq = _increase_precision(gq, pol_gq, div(f.precision+e-1, e), ex, P)
     f.inv_img = (gq, f.inv_img[2])
 
-    Zp = maximal_order(prime_field(Kp))
+    Zp = maximal_order(absolute_base_field(Kp))
     Qq = base_field(Kp)
 
     setprecision!(Qq, ex)
@@ -384,7 +384,7 @@ function totally_ramified_completion(K::AbsSimpleNumField, P::AbsNumFieldOrderId
   @assert nf(OK) == K
   @assert isone(degree(P))
   e = ramification_index(P)
-  Qp = PadicField(minimum(P), precision)
+  Qp = padic_field(minimum(P), precision = precision)
   Zp = maximal_order(Qp)
   Zx = FlintZZ["x"][1]
   Qpx = polynomial_ring(Qp, "x")[1]
@@ -443,7 +443,7 @@ function setprecision!(f::CompletionMap{LocalField{PadicFieldElem, EisensteinLoc
     if r > 0
       ex += 1
     end
-    Qp = PadicField(prime(Kp), div(new_prec, e)+1)
+    Qp = padic_field(prime(Kp), precision = div(new_prec, e) + 1)
     Zp = maximal_order(Qp)
     Qpx, _ = polynomial_ring(Qp, "x")
     pows_u = powers(u, e-1)
@@ -495,8 +495,8 @@ function unramified_completion(K::AbsSimpleNumField, P::AbsNumFieldOrderIdeal{Ab
   @assert isone(ramification_index(P))
   f = degree(P)
   p = minimum(P)
-  Qq, gQq = QadicField(p, f, precision)
-  Qp = PadicField(p, precision)
+  Qq, gQq = qadic_field(p, f, precision = precision)
+  Qp = padic_field(p, precision = precision)
   Zp = maximal_order(Qp)
   q, mq = residue_field(Qq)
   F, mF = residue_field(OK, P)

src/LocalField/Conjugates.jl

@@ -1,5 +1,5 @@
 #XXX: valuation(Q(0)) == 0 !!!!!
-function newton_lift(f::ZZPolyRingElem, r::QadicFieldElem, prec::Int = parent(r).prec_max, starting_prec::Int = 2)
+function newton_lift(f::ZZPolyRingElem, r::QadicFieldElem, prec::Int = precision(parent(r)), starting_prec::Int = 2)
   Q = parent(r)
   n = prec
   i = n
@@ -19,22 +19,22 @@ function newton_lift(f::ZZPolyRingElem, r::QadicFieldElem, prec::Int = parent(r)
   for p = reverse(chain)
     setprecision!(r, p)
     setprecision!(o, p)
-    Q.prec_max = r.N
+    setprecision!(Q, r.N)
     if r.N > precision(Q)
       setprecision!(qf, r.N)
       setprecision!(qfs, r.N)
     end
     r = r - qf(r)*o
     if r.N >= n
-      Q.prec_max = n
+      setprecision!(Q, n)
       return r
     end
     o = o*(2-qfs(r)*o)
   end
   return r
 end
 
-function newton_lift(f::ZZPolyRingElem, r::LocalFieldElem, precision::Int = parent(r).prec_max, starting_prec::Int = 2)
+function newton_lift(f::ZZPolyRingElem, r::LocalFieldElem, precision::Int = precision(parent(r)), starting_prec::Int = 2)
   Q = parent(r)
   n = precision
   i = n
@@ -93,7 +93,7 @@ function roots(C::qAdicRootCtx, n::Int = 10)
   lf = factor_mod_pk(Array, C.H, n)
   rt = QadicFieldElem[]
   for Q = C.Q
-    Q.prec_max = n
+    setprecision!(Q, n)
     for x = lf
       if is_splitting(C) || degree(x[1]) == degree(Q)
         append!(rt, roots(Q, x[1], max_roots = 1))

src/LocalField/Elem.jl

@@ -856,7 +856,7 @@ function divexact(a::LocalFieldElem, b::Union{Integer, ZZRingElem}; check::Bool=
   e = absolute_ramification_index(K)
   v = valuation(b, p)
   iszero(a) && return setprecision(a, precision(a) - v*e)
-  Qp = prime_field(K)
+  Qp = absolute_base_field(K)
   old = precision(Qp)
   setprecision!(Qp, e*precision(a)+ Int(_valuation_integral(a)) + v)
   bb = inv(Qp(b))

src/LocalField/LocalField.jl

@@ -134,15 +134,6 @@ end
 #
 ################################################################################
 
-function prime_field(L::Union{QadicField, LocalField})
-  L = base_ring(defining_polynomial(L))
-  while typeof(L) != PadicField
-    L = base_ring(defining_polynomial(L))
-  end
-  return L
-end
-
-
 function base_field(L::LocalField)
   return base_ring(defining_polynomial(L))
 end
@@ -366,7 +357,7 @@ end
 
 function local_field(f::QQPolyRingElem, p::Int, precision::Int, s::VarName, ::Type{T} = GenericLocalField; check::Bool = true, cached::Bool = true) where T <: LocalFieldParameter
   @assert is_prime(p)
-  K = PadicField(p, precision)
+  K = padic_field(p, precision = precision)
   fK = map_coefficients(K, f, cached = false)
   return local_field(fK, s, T, cached = cached, check = check)
 end

src/LocalField/Poly.jl

@@ -49,7 +49,7 @@ function setcoeff!(c::Generic.Poly{T}, n::Int, a::T) where {T <: Union{PadicFiel
 end
 
 #TODO: find better crossover points
-#  qp = PadicField(3, 10);
+#  qp = padic_field(3, precision = 10);
 #  qpt, t = qp["t"]
 #  E = eisenstein_extension(cyclotomic(3, gen(Hecke.Globals.Zx))(t+1))[1]
 #  Es, s = E["s"]
@@ -711,8 +711,6 @@ function _rres(f::Generic.Poly{T}, g::Generic.Poly{T}) where T <: Union{PadicFie
   return res*res1
 end
 
-base_field(Q::QadicField) = base_ring(defining_polynomial(Q))
-
 function norm(f::PolyRingElem{T}) where T <: Union{QadicFieldElem, LocalFieldElem}
   Kx = parent(f)
   K = base_ring(f)
@@ -749,7 +747,7 @@ function characteristic_polynomial(f::Generic.Poly{T}, g::Generic.Poly{T}) where
       error("Not yet implemented")
     end
     d1 = clog(ZZRingElem(degree(f)+1), p)
-    L = QadicField(p, d1, min(precision(f), precision(g)))
+    L = qadic_field(p, d1, precision = min(precision(f), precision(g)))
     Lt = polynomial_ring(L, "t")[1]
     fL = map_coefficients(L, f, parent = Lt)
     gL = map_coefficients(L, g, parent = Lt)

src/LocalField/Ring.jl

@@ -99,9 +99,7 @@ end
 #
 ################################################################################
 
-coefficient_ring(Q::LocalFieldValuationRing) = ring_of_integers(coefficient_ring(_field(Q)))
-
-coefficient_ring(K::LocalField) = base_field(K)
+coefficient_ring(Q::LocalFieldValuationRing) = valuation_ring(base_field(_field(Q)))
 
 function absolute_coordinates(a::LocalFieldValuationRingElem)
   v = absolute_coordinates(data(a))

src/LocalField/neq.jl

@@ -214,7 +214,7 @@ function coordinates(a::Union{QadicFieldElem, LocalFieldElem}, k)
   return c
 end
 coordinates(a::PadicFieldElem, ::PadicField) = [a]
-lift(a::Hecke.LocalFieldValuationRingElem{PadicField, PadicFieldElem}) = lift(a.x)
+lift(R::Ring, a::Hecke.LocalFieldValuationRingElem{PadicField, PadicFieldElem}) = lift(R, a.x)
 
 function setprecision!(A::Generic.MatSpaceElem{Hecke.LocalFieldValuationRingElem{PadicField, PadicFieldElem}}, n::Int)
   for i=1:nrows(A)
@@ -255,7 +255,7 @@ function solve_1_units(a::Vector{T}, b::T) where T
   cur_a = copy(a)
   cur_b = b
 #  @assert degree(K) == e
-  Qp = prime_field(K)
+  Qp = absolute_base_field(K)
   Zp = ring_of_integers(Qp)
   expo_mult = identity_matrix(ZZ, length(cur_a))
   #transformation of cur_a to a
@@ -565,7 +565,7 @@ struct MapEvalCtx
   map::Generic.MatSpaceElem{PadicFieldElem}
 
   function MapEvalCtx(M::LocalFieldMor)
-    mat = matrix(prime_field(domain(M)),
+    mat = matrix(absolute_base_field(domain(M)),
                  absolute_degree(domain(M)),
                  absolute_degree(codomain(M)),
                  reduce(vcat, [absolute_coordinates(M(x))
@@ -778,7 +778,7 @@ function local_fundamental_class_serre(mKL::LocalFieldMor)
     #thus Gal(E/base_field(L)) = Gal(L/base_field(L)) x unram of base_field
     bL = base_field(L)
     E2, _ = unramified_extension(map_coefficients(x->bL(coeff(x, 0)), defining_polynomial(E), cached = false))
-    G2 = automorphism_list(E2, prime_field(E2))
+    G2 = automorphism_list(E2, absolute_base_field(E2))
     GG = morphism_type(E)[]
     for e = G2
       ime = e(gen(E2))
@@ -794,7 +794,7 @@ function local_fundamental_class_serre(mKL::LocalFieldMor)
     @assert length(GG) == divexact(absolute_degree(E), absolute_degree(K))
 #    @assert all(x->x in GG, automorphism_list(E, K))
   else
-    GG = automorphism_list(E, prime_field(E))
+    GG = automorphism_list(E, absolute_base_field(E))
     gK = map(E, gK)
     GG = [g for g = GG if map(g, gK) == gK]
   end
@@ -828,7 +828,7 @@ function local_fundamental_class_serre(mKL::LocalFieldMor)
   beta = []
   sigma_hat = []
   #need to map and compare all generators
-  gL = gens(L, prime_field(L))
+  gL = gens(L, absolute_base_field(L))
   imGG = map(x->map(x, map(E, gL)), GG)
   imG = map(x->map(x, gL), G)
 
@@ -1367,7 +1367,7 @@ function is_local_norm(k::Hecke.AbsSimpleNumField, a::ZZRingElem)
       end
       continue
     end
-    Qp = PadicField(p, prec)
+    Qp = padic_field(p, precision = prec)
     #for each P we need
     # - a gen (pi) for the valuation
     # - a gen for the residue field

src/LocalField/pAdic.jl

@@ -41,7 +41,7 @@ function my_log_one_minus(x::PadicFieldElem)
   pp = prime(parent(x), 2)
   X = 1-x
   while true
-    y = lift(1-X) % pp
+    y = lift(ZZ, 1-X) % pp
     lg += parent(x)(my_log_one_minus_inner(y, precision(x), le, prime(parent(x))))
     X = X*inv(parent(x)(1-y))
     pp *= pp
@@ -76,10 +76,10 @@ function my_log_one_minus(x::QadicFieldElem)
   pp = prime(parent(x))^2
   X = 1-x
   R, _ = polynomial_ring(QQ, cached = false)
-  S, _ = residue_ring(R, map_coefficients(x->QQ(lift(x)), defining_polynomial(parent(x)), parent = R))
+  S, _ = residue_ring(R, map_coefficients(x->QQ(lift(ZZ, x)), defining_polynomial(parent(x)), parent = R))
   while true
     Y = 1-X
-    y = S(R([lift(coeff(Y, i)) % pp for i=0:length(Y)]))
+    y = S(R([lift(ZZ, coeff(Y, i)) % pp for i=0:length(Y)]))
     lg += parent(x)(my_log_one_minus_inner(y, precision(x), le, prime(parent(x))).data)
     X = X*inv(parent(x)(1-y.data))
     pp *= pp

src/LocalField/qAdic.jl

@@ -57,8 +57,6 @@ function residue_field(Q::PadicField)
   return k, mp
 end
 
-coefficient_field(Q::QadicField) = coefficient_ring(Q)
-
 function getUnit(a::PadicFieldElem)
   u = ZZRingElem()
   ccall((:fmpz_set, libflint), Cvoid, (Ref{ZZRingElem}, Ref{Int}), u, a.u)
@@ -79,7 +77,7 @@ function lift_reco(::QQField, a::PadicFieldElem; reco::Bool = false)
       return x*prime(R, v)
     end
   else
-    return lift(FlintQQ, a)
+    return lift(QQ, a)
   end
 end
 
@@ -88,7 +86,7 @@ uniformizer(Q::QadicField) = Q(prime(Q))
 
 uniformizer(Q::PadicField) = Q(prime(Q))
 
-function defining_polynomial(Q::QadicField, P::Ring = coefficient_ring(Q))
+function defining_polynomial(Q::QadicField, P::Ring = base_field(Q))
   Pt, t = polynomial_ring(P, cached = false)
   f = Pt()
   for i=0:Q.len-1

src/Misc/UnitsModM.jl

@@ -280,7 +280,7 @@ function disc_log_mod(a::ZZRingElem, b::ZZRingElem, M::ZZRingElem)
       @assert (b-1) % 8 == 0
       @assert (a^2-1) % 8 == 0
       if fM[p] > 3
-        F = PadicField(p, fM[p], cached = false)
+        F = padic_field(p, precision = fM[p], cached = false)
         g += 2*lift(divexact(log(F(b)), log(F(a^2))))
       end
       return g

src/NumField/NfAbs/MPolyAbsFact.jl

@@ -865,7 +865,7 @@ function field(RC::RootCtx, m::MatElem)
 
   @vprintln :AbsFact 1 "target field has (local) degree $k"
 
-  Qq = QadicField(characteristic(F), k, 1, cached = false)[1]
+  Qq = qadic_field(characteristic(F), k, precision = 1, cached = false)[1]
   Qqt = polynomial_ring(Qq, cached = false)[1]
   k, mk = residue_field(Qq)
 

src/QuadForm/Quad/NormalForm.jl

@@ -208,7 +208,7 @@ function _padic_normal_form(G::QQMatrix, p::ZZRingElem; prec::Int = -1, partial:
 
   n = ncols(Gmod)
 
-  Qp = PadicField(p, prec, cached = false)
+  Qp = padic_field(p, precision = prec, cached = false)
 
   if n == 0
     return (zero_matrix(FlintQQ, n, n), zero_matrix(FlintQQ, n, n))::Tuple{QQMatrix, QQMatrix}