Add basic functionality for univariate Ore operators

src/AbstractTypes.jl

@@ -76,6 +76,8 @@ abstract type IdentityMap <: SetMap end
 
 abstract type FPModuleHomomorphism <: FunctionalMap end
 
+abstract type SkewDerivation{D,S} <: Map{D,D,Map,SkewDerivation} where {S<:Map{D,D}} end
+
 # rings, fields etc, parameterised by an element type
 # these are the type classes of different kinds of
 # mathematical rings/fields/etc, which have a base ring,
@@ -106,6 +108,8 @@ abstract type MatRing{T<:NCRingElement} <: NCRing end
 
 abstract type FreeAssociativeAlgebra{T<:RingElement} <: NCRing end
 
+abstract type OreAlgebra{T<:RingElement} <: NCPolyRing{T} end
+
 # Abstract types for number fields, parmeterised by the element type of
 # the base field.
 abstract type NumField{T<:RingElement} <: Field end
@@ -151,6 +155,8 @@ abstract type MatRingElem{T<:NCRingElement} <: NCRingElem end
 
 abstract type FreeAssociativeAlgebraElem{T<:RingElement} <: NCRingElem end
 
+abstract type OreOperator{T<:RingElem} <: NCPolyRingElem{T} end
+
 abstract type NumFieldElem{T<:RingElement} <: FieldElem end
 
 abstract type SimpleNumFieldElem{T} <: NumFieldElem{T} end

src/Generic.jl

@@ -94,6 +94,10 @@ include("generic/FreeAssociativeAlgebraGroebner.jl")
 
 include("generic/PolyRingHom.jl")
 
+include("generic/OreAlgebras.jl")
+include("generic/PolySkewDerivation.jl")
+include("generic/PolyFracFieldHom.jl")
+
 ###############################################################################
 #
 #   Temporary miscellaneous files being moved from Hecke.jl

src/exports.jl

@@ -620,3 +620,11 @@ export zero!
 export zero_matrix
 export zeros
 export zz
+
+export ore_extension
+export trivial_derivation
+export derivation
+export sigma_endomorphism
+export OreAlgebra
+export OreOperator
+export SkewDerivation

src/generic/GenericTypes.jl

@@ -1607,3 +1607,64 @@ end
 function PolyRingAnyMap(d::D, c::C, cm::U, ig::V) where {D, C, U, V}
   return PolyRingAnyMap{D, C, U, V}(d, c, cm, ig)
 end
+
+################################################################################
+#
+#   R-algebra morphisms of R(x)
+#
+################################################################################
+
+mutable struct PolyFracFieldAnyMap{
+    D <: Union{FracField{<:PolyRingElem},RationalFunctionField{<:RingElement,<:PolyRingElem}},
+    C <: NCRing,
+    V <: Map{<:PolyRing,C}} <: Map{D,C,Map,PolyFracFieldAnyMap}
+
+  domain::D
+  morphism::V
+
+  function PolyFracFieldAnyMap{D,C,V}(d::D,phi::V) where {D,C,V}
+    return new{D,C,V}(d,phi)
+  end
+end
+
+function PolyFracFieldAnyMap(d::D,i::V) where {D,C,V<:Map{<:PolyRing,C}}
+  return PolyFracFieldAnyMap{D,C,V}(d,i)
+end
+
+
+################################################################################
+#
+#   Univariate Ore algebra, its element type skew derivations
+#
+################################################################################
+@attributes mutable struct OreAlgebra{T<:RingElem} <: AbstractAlgebra.OreAlgebra{T}
+  base_ring::Ring
+  D::Symbol
+  δ::Map(SkewDerivation)
+
+  function OreAlgebra{T}(R::Ring, D::Symbol, δ; cached=true) where T<:RingElem
+    return get_cached!(OreID, (R,D,δ), cached) do
+      new{T}(R,D,δ)
+    end
+  end
+end
+
+const OreID = CacheDictType{Tuple{Ring,Symbol,Map(SkewDerivation)},NCRing}()
+
+mutable struct OreOperator{T<:RingElem} <: AbstractAlgebra.OreOperator{T}
+  parent::OreAlgebra{T}
+  coeffs::Vector{T}
+  length::Int
+end
+
+mutable struct PolySkewDerivation{D,S} <: SkewDerivation{D,S}
+  domain::D
+  σ::S
+  intermediate_cache::Vector{<:NCRingElem}
+
+  function PolySkewDerivation{D,S}(dom::D,σ::S,coeff::T) where {D,S,T<:NCRingElem}
+    return new{D,S}(dom,σ,[coeff])
+  end
+end
+
+Univariateish = Union{PolyRing,FracField{<:PolyRingElem},RationalFunctionField}