Add several is_known methods for characteristic and is_perfect

src/AbsMSeries.jl

@@ -40,9 +40,8 @@ $R$.
 """
 symbols(R::MSeriesRing)
 
-function characteristic(a::MSeriesRing)
-    return characteristic(base_ring(a))
-end
+characteristic(R::MSeriesRing) = characteristic(base_ring(R))
+is_known(::typeof(characteristic), R::MSeriesRing) = is_known(characteristic, base_ring(R))
 
 ###############################################################################
 #

src/Fraction.jl

@@ -20,9 +20,8 @@ function is_exact_type(a::Type{T}) where {S <: RingElement, T <: FracElem{S}}
    return is_exact_type(S)
 end
 
-function characteristic(R::FracField{T}) where T <: RingElem
-   return characteristic(base_ring(R))
-end
+characteristic(R::FracField) = characteristic(base_ring(R))
+is_known(::typeof(characteristic), R::FracField) = is_known(characteristic, base_ring(R))
 
 @doc raw"""
     vars(a::FracElem{S}) where {S <: MPolyRingElem{<: RingElement}}

src/FreeAssociativeAlgebra.jl

@@ -22,6 +22,7 @@ function is_exact_type(a::Type{S}) where {T <: RingElement, S <: FreeAssociative
 end
 
 characteristic(R::FreeAssociativeAlgebra) = characteristic(base_ring(R))
+is_known(::typeof(characteristic), R::FreeAssociativeAlgebra) = is_known(characteristic, base_ring(R))
 
 is_finite(R::FreeAssociativeAlgebra) = is_trivial(base_ring(R)) || (nvars(R) == 0 && is_finite(base_ring(R)))
 

src/LaurentPoly.jl

@@ -11,6 +11,7 @@
 ###############################################################################
 
 characteristic(R::LaurentPolyRing) = characteristic(base_ring(R))
+is_known(::typeof(characteristic), R::LaurentPolyRing) = is_known(characteristic, base_ring(R))
 
 is_finite(R::LaurentPolyRing) = is_trivial(R)
 

src/MatRing.jl

@@ -65,11 +65,8 @@ function is_zero_divisor_with_annihilator(a::MatRingElem{T}) where T <: RingElem
    throw(NotImplementedError(:adj, a)) #return f, b*adj(A)
 end
 
-
-function characteristic(a::MatRing)
-   iszero(nrows(a)) && return 1
-   return characteristic(base_ring(a))
-end
+characteristic(R::MatRing) = iszero(nrows(R)) ? 1 : characteristic(base_ring(R))
+is_known(::typeof(characteristic), R::MatRing) = iszero(nrows(R)) || is_known(characteristic, base_ring(R))
 
 is_finite(R::MatRing) = iszero(nrows(R)) || is_finite(base_ring(R))
 

src/NCPoly.jl

@@ -102,7 +102,8 @@ Return the number of variables of the polynomial ring, which is 1.
 """
 number_of_variables(a::NCPolyRing) = 1
 
-characteristic(a::NCPolyRing) = characteristic(base_ring(a))
+characteristic(R::NCPolyRing) = characteristic(base_ring(R))
+is_known(::typeof(characteristic), R::NCPolyRing) = is_known(characteristic, base_ring(R))
 
 is_finite(a::NCPolyRing) = is_trivial(a)
 

src/NumFields.jl

@@ -8,6 +8,7 @@ end
 number_of_generators(L::SimpleNumField{T}) where {T} = 1
 
 characteristic(F::NumField) = 0
+is_known(::typeof(characteristic), F::NumField) = true
 
 promote_rule(::Type{T}, ::Type{S}) where {S<:NumFieldElem,T<:Integer} = S
 

src/Poly.jl

@@ -48,7 +48,8 @@ Return the number of variables of the polynomial ring, which is 1.
 """
 number_of_variables(a::PolyRing) = 1
 
-characteristic(a::PolyRing) = characteristic(base_ring(a))
+characteristic(R::PolyRing) = characteristic(coefficient_ring(R))
+is_known(::typeof(characteristic), R::PolyRing) = is_known(characteristic, coefficient_ring(R))
 
 is_finite(a::PolyRing) = is_trivial(a)
 

src/Residue.jl

@@ -113,9 +113,8 @@ annihilator(a::ResElem) = is_zero_divisor_with_annihilator(a)[2]
 deepcopy_internal(a::ResElem, dict::IdDict) =
    parent(a)(deepcopy_internal(data(a), dict))
 
-function characteristic(a::ResidueRing{T}) where T <: Integer
-   return modulus(a)
-end
+characteristic(R::ResidueRing{T}) where T <: Integer = modulus(R)
+is_known(::typeof(characteristic), R::ResidueRing{T}) where T <: Integer = true
 
 ###############################################################################
 #

src/ResidueField.jl

@@ -64,13 +64,8 @@ function modulus(r::ResFieldElem)
    return modulus(parent(r))
 end
 
-function characteristic(R::ResidueField)
-   return characteristic(base_ring(R))
-end
-
-function characteristic(r::ResidueField{T}) where T <: Integer
-   return modulus(r)
-end
+characteristic(r::ResidueField{T}) where T <: Integer = modulus(r)
+is_known(::typeof(characteristic), R::ResidueField{T}) where T <: Integer = true
 
 data(a::ResFieldElem) = a.data
 

src/Rings.jl

@@ -195,6 +195,7 @@ of a single element, or equivalently if its characteristic is 1. Such
 rings are also called zero rings.
 """
 is_trivial(R::NCRing) = !is_domain_type(elem_type(R)) && iszero(one(R))
+is_known(::typeof(is_trivial), R::NCRing) = is_domain_type(elem_type(R))
 
 @doc raw"""
     is_zero(R::NCRing)
@@ -223,8 +224,11 @@ is_zero(R::NCRing) = is_trivial(R)
 Test whether the field $F$ is perfect, that is, whether the characteristic is zero or
 else whether every element of $F$ admits a $p$-th root, where $p > 0$ is the characteristic of $F$.
 """
-is_perfect(F::Field) = characteristic(F) == 0 || F isa FinField ||
-                                                 throw(NotImplementedError(:is_perfect, F))
+is_perfect(F::Field) = characteristic(F) == 0 || throw(NotImplementedError(:is_perfect, F))
+is_known(::typeof(is_perfect), F::Field) = is_known(characteristic, F) && characteristic(F) == 0
+
+is_perfect(F::FinField) = true
+is_known(::typeof(is_perfect), F::FinField) = true
 
 is_finite(F::FinField) = true
 

src/generic/AbsSeries.jl

@@ -70,9 +70,8 @@ function deepcopy_internal(a::AbsSeries{T}, dict::IdDict) where T <: RingElement
    return parent(a)(coeffs, length(a), precision(a))
 end
 
-function characteristic(a::AbsPowerSeriesRing{T}) where T <: RingElement
-   return characteristic(base_ring(a))
-end
+characteristic(R::AbsPowerSeriesRing) = characteristic(base_ring(R))
+is_known(::typeof(characteristic), R::AbsPowerSeriesRing) = is_known(characteristic, base_ring(R))
 
 ###############################################################################
 #

src/generic/FactoredFraction.jl

@@ -20,7 +20,8 @@ base_ring_type(::Type{FactoredFracField{T}}) where T <: NCRingElement = parent_t
 
 base_ring(F::FactoredFracField{T}) where T <: RingElement = F.base_ring::parent_type(T)
 
-characteristic(F::FactoredFracField{T}) where T <: RingElement = characteristic(base_ring(F))
+characteristic(F::FactoredFracField) = characteristic(base_ring(F))
+is_known(::typeof(characteristic), R::FactoredFracField) = is_known(characteristic, base_ring(R))
 
 ###############################################################################
 #

src/generic/FunctionField.jl

@@ -556,6 +556,7 @@ symbol.
 var(R::FunctionField) = R.S
 
 characteristic(R::FunctionField) = characteristic(base_ring(R))
+is_known(::typeof(characteristic), R::FunctionField) = is_known(characteristic, base_ring(R))
 
 is_perfect(R::FunctionField) = characteristic(R) == 0
 

src/generic/LaurentPoly.jl

@@ -31,6 +31,7 @@ number_of_variables(R::LaurentPolyWrapRing) = 1
 number_of_generators(R::LaurentPolyWrapRing) = number_of_variables(R)
 
 characteristic(R::LaurentPolyWrapRing) = characteristic(R.polyring)
+is_known(::typeof(characteristic), R::LaurentPolyWrapRing) = is_known(characteristic, base_ring(R))
 
 
 ###############################################################################

src/generic/LaurentSeries.jl

@@ -373,9 +373,8 @@ function renormalize!(z::LaurentSeriesElem)
    return nothing
 end
 
-function characteristic(a::LaurentSeriesRing{T}) where T <: RingElement
-   return characteristic(base_ring(a))
-end
+characteristic(R::LaurentSeriesRing) = characteristic(base_ring(R))
+is_known(::typeof(characteristic), R::LaurentSeriesRing) = is_known(characteristic, base_ring(R))
 
 ###############################################################################
 #

src/generic/PuiseuxSeries.jl

@@ -267,9 +267,8 @@ function deepcopy_internal(a::PuiseuxSeriesElem{T}, dict::IdDict) where {T <: Ri
     return parent(a)(deepcopy_internal(a.data, dict), a.scale)
 end
 
-function characteristic(a::PuiseuxSeriesRing{T}) where T <: RingElement
-   return characteristic(base_ring(a))
-end
+characteristic(R::PuiseuxSeriesRing) = characteristic(base_ring(R))
+is_known(::typeof(characteristic), R::PuiseuxSeriesRing) = is_known(characteristic, base_ring(R))
 
 ###############################################################################
 #

src/generic/RationalFunctionField.jl

@@ -132,9 +132,8 @@ function deepcopy_internal(a::RationalFunctionFieldElem, dict::IdDict)
    return R(deepcopy_internal(data(a), dict))
 end
 
-function characteristic(R::RationalFunctionField)
-   return characteristic(base_ring(R))
-end
+characteristic(R::RationalFunctionField) = characteristic(base_ring(R))
+is_known(::typeof(characteristic), R::RationalFunctionField) = is_known(characteristic, base_ring(R))
 
 is_finite(R::RationalFunctionField) = is_finite(base_ring(underlying_fraction_field(R)))
 

src/generic/RelSeries.jl

@@ -60,9 +60,8 @@ function deepcopy_internal(a::RelSeries{T}, dict::IdDict) where T <: RingElement
    return parent(a)(coeffs, pol_length(a), precision(a), valuation(a))
 end
 
-function characteristic(a::RelPowerSeriesRing{T}) where T <: RingElement
-   return characteristic(base_ring(a))
-end
+characteristic(R::RelPowerSeriesRing) = characteristic(base_ring(R))
+is_known(::typeof(characteristic), R::RelPowerSeriesRing) = is_known(characteristic, base_ring(R))
 
 ###############################################################################
 #

src/generic/Residue.jl

@@ -114,8 +114,9 @@ function gens(R::Union{EuclideanRingResidueRing{T}, EuclideanRingResidueField{T}
 end
 
 function characteristic(R::Union{EuclideanRingResidueRing{T}, EuclideanRingResidueField{T}}) where {T<:PolyRingElem}
-   return characteristic(base_ring(base_ring(R)))
+   return characteristic(base_ring(R))
 end
+is_known(::typeof(characteristic), R::Union{EuclideanRingResidueRing{T}, EuclideanRingResidueField{T}}) where {T<:PolyRingElem} = is_known(characteristic, base_ring(R))
 
 function size(R::Union{EuclideanRingResidueRing{T}, EuclideanRingResidueField{T}}) where {T<:PolyRingElem}
    return size(base_ring(base_ring(R)))^degree(modulus(R))

src/generic/SparsePoly.jl

@@ -83,9 +83,8 @@ function deepcopy_internal(a::SparsePoly{T}, dict::IdDict) where {T <: RingEleme
    return parent(a)(Rc, Re)
 end
 
-function characteristic(a::SparsePolyRing{T}) where T <: RingElement
-   return characteristic(base_ring(a))
-end
+characteristic(R::SparsePolyRing) = characteristic(base_ring(R))
+is_known(::typeof(characteristic), R::SparsePolyRing) = is_known(characteristic, base_ring(R))
 
 ###############################################################################
 #

src/generic/TotalFraction.jl

@@ -34,9 +34,8 @@ function is_exact_type(a::Type{T}) where {S <: RingElem, T <: TotFrac{S}}
    return is_exact_type(S)
 end
 
-function characteristic(R::TotFracRing{T}) where T <: RingElem
-   return characteristic(base_ring(R))
-end
+characteristic(R::TotFracRing) = characteristic(base_ring(R))
+is_known(::typeof(characteristic), R::TotFracRing) = is_known(characteristic, base_ring(R))
 
 ###############################################################################
 #

src/generic/UnivPoly.jl

@@ -280,6 +280,7 @@ end
 canonical_unit(p::UnivPoly) = canonical_unit(data(p))
 
 characteristic(R::UniversalPolyRing) = characteristic(coefficient_ring(R))
+is_known(::typeof(characteristic), R::UniversalPolyRing) = is_known(characteristic, coefficient_ring(R))
 
 function Base.hash(p::UnivPoly, h::UInt)
    b = 0xcf418d4529109236%UInt

src/julia/Float.jl

@@ -40,7 +40,8 @@ is_unit(a::AbstractFloat) = !is_zero(a)
 
 canonical_unit(a::AbstractFloat) = iszero(a) ? copysign(one(a), a) : a
 
-characteristic(a::Floats{T}) where T <: AbstractFloat = 0
+characteristic(::Floats) = 0
+is_known(::typeof(characteristic), ::Floats) = true
 
 if VERSION < v"1.13.0-DEV.534" # https://github.com/JuliaLang/julia/pull/53677
   is_negative(n::T) where T<:Real = n < zero(T)

src/julia/GF.jl

@@ -73,9 +73,8 @@ isone(a::GFElem{T}) where T <: Integer = a.d == 1
 
 is_unit(a::GFElem) = a.d != 0
 
-function characteristic(R::GFField)
-   return R.p
-end
+characteristic(R::GFField) = R.p
+is_known(::typeof(characteristic), ::GFField) = true
 
 @doc raw"""
     order(R::GFField)

src/julia/Integer.jl

@@ -44,7 +44,8 @@ is_zero_divisor(a::Integer) = is_zero(a)
 
 canonical_unit(a::T) where T <: Integer = a < 0 ? T(-1) : T(1)
 
-characteristic(::Integers{T}) where T <: Integer = 0
+characteristic(::Integers) = 0
+is_known(::typeof(characteristic), ::Integers) = true
 
 ###############################################################################
 #

src/julia/Rational.jl

@@ -52,7 +52,8 @@ function denominator(a::Rational, canonicalise::Bool=true)
    return Base.denominator(a) # all other types ignore canonicalise
 end
 
-characteristic(a::Rationals{T}) where T <: Integer = 0
+characteristic(::Rationals) = 0
+is_known(::typeof(characteristic), ::Rationals) = true
 
 ###############################################################################
 #