coefficient_ring -> base_field for the p-adics (#1605)

Author: joschmitt

src/Deprecations.jl

@@ -274,9 +274,9 @@ end
 
 @deprecate rres reduced_resultant
 
-# To be deprecated in 0.34.0
+# Deprecated in 0.34.0
 
-#@deprecate lift(a::LocalFieldValuationRingElem) lift(ZZ, a)
-lift(a::LocalFieldValuationRingElem) = lift(ZZ, a)
-#@deprecate prime_field(L::Union{QadicField, LocalField}) absolute_base_field(L)
-prime_field(L::Union{QadicField, LocalField}) = absolute_base_field(L)
+@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/LocalField/Poly.jl

@@ -709,8 +709,6 @@ 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)

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/qAdic.jl

@@ -54,8 +54,6 @@ 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)
@@ -85,7 +83,7 @@ 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