Add residue ring of local fields (thofma#1529)

joschmitt · May 29, 2024 · b8b8e29 · b8b8e29
1 parent 6d9b2ee
commit b8b8e29
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Showing 12 changed files with 593 additions and 96 deletions.
diff --git a/examples/NFDB.jl b/examples/NFDB.jl
@@ -1195,7 +1195,7 @@ function _p_adic_regulator_coates(K::AbsSimpleNumField, p::IntegerUnion)
   # working_prec.
   while true
     (prec > 2^12 || working_prec > 2^12) && error("Something wrong")
-    imK =[QadicRingElem{PadicField, PadicFieldElem}[] for i in 1:degK]
+    imK =[LocalFieldValuationRingElem{PadicField, PadicFieldElem}[] for i in 1:degK]
     Qp = PadicField(p, prec, cached = false)
     Zp = ring_of_integers(Qp)
     dK = discriminant(OK)

diff --git a/src/LocalField.jl b/src/LocalField.jl
@@ -9,3 +9,4 @@ include("LocalField/Conjugates.jl")
 include("LocalField/Poly.jl")
 include("LocalField/Completions.jl")
 include("LocalField/neq.jl")
+include("LocalField/ResidueRing.jl")
diff --git a/src/LocalField/Elem.jl b/src/LocalField/Elem.jl
@@ -25,6 +25,10 @@ function Base.deepcopy_internal(x::LocalFieldElem{S, T}, dict::IdDict) where {S,
   return LocalFieldElem{S, T}(parent(x), Base.deepcopy_internal(x.data, dict), precision(x))
 end
 
+function Base.hash(a::LocalFieldElem, h::UInt)
+  return hash(a.data, h)
+end
+
 ################################################################################
 #
 #  Precision
@@ -235,22 +239,21 @@ function O(K::LocalField, prec::T) where T <: IntegerUnion
   return K(O(base_field(K), d))
 end
 
-function zero(K::LocalField)
+function zero(K::LocalField; precision=precision(K))
   a = zero(parent(defining_polynomial(K)))
-  return setprecision(K(a), precision(K))
+  return setprecision(K(a), precision)
 end
 
 (K::LocalField)() = zero(K)
 
-function one(K::LocalField)
+function one(K::LocalField; precision=precision(K))
   a = one(parent(defining_polynomial(K)))
-  return setprecision(K(a), precision(K))
+  return setprecision(K(a), precision)
 end
 
-function zero!(a::LocalFieldElem)
-  K = parent(a)
+function zero!(a::LocalFieldElem; precision=precision(parent(a)))
   zero!(a.data)
-  a.data = setprecision(a.data, precision(K))
+  a.data = setprecision(a.data, precision)
   return a
 end
 
@@ -283,14 +286,14 @@ end
 #
 ################################################################################
 
-function (K::LocalField{S, T})(a::Integer) where {S <: FieldElem, T <: LocalFieldParameter}
+function (K::LocalField{S, T})(a::Integer; precision=precision(K)) where {S <: FieldElem, T <: LocalFieldParameter}
   el =  K(parent(defining_polynomial(K))(a))
-  return setprecision!(el, precision(K))
+  return setprecision!(el, precision)
 end
 
-function (K::LocalField{S, T})(a::Union{ZZRingElem, QQFieldElem}) where {S <: FieldElem, T <: LocalFieldParameter}
+function (K::LocalField{S, T})(a::Union{ZZRingElem, QQFieldElem}; precision=precision(K)) where {S <: FieldElem, T <: LocalFieldParameter}
   el =  K(parent(defining_polynomial(K))(a))
-  return setprecision!(el, precision(K))
+  return setprecision!(el, precision)
 end
 
 function (K::LocalField{S, T})(a::U) where {U <: Union{PadicFieldElem, QadicFieldElem}, S <: FieldElem, T <: LocalFieldParameter}