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Add is_euclidean_type trait #1943

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Add is_euclidean_type trait #1943

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28b0cb3
Make is_exact_type and is_domain_type more convenient
fingolfin Dec 20, 2024
f5d43f0
Add is_euclidean_type trait
fingolfin Dec 20, 2024
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2 changes: 2 additions & 0 deletions src/Fields.jl
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Expand Up @@ -6,6 +6,8 @@

is_domain_type(::Type{T}) where {T <: FieldElem} = true

is_euclidean_type(::Type{T}) where {T <: FieldElem} = true

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is_zero_divisor(a::T) where T <: FieldElem = is_zero(a)

is_unit(a::FieldElem) = !iszero(a)
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11 changes: 5 additions & 6 deletions src/Poly.jl
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Expand Up @@ -16,13 +16,12 @@

dense_poly_type(::Type{T}) where T<:RingElement = Generic.Poly{T}

function is_domain_type(::Type{T}) where {S <: RingElement, T <: PolyRingElem{S}}
return is_domain_type(S)
end
is_exact_type(::Type{<:PolyRingElem{T}}) where {T <: RingElement} = is_exact_type(T)

function is_exact_type(a::Type{T}) where {S <: RingElement, T <: PolyRingElem{S}}
return is_exact_type(S)
end
is_domain_type(::Type{<:PolyRingElem{T}}) where {T <: RingElement} = is_domain_type(T)

is_euclidean_type(::Type{<:PolyRingElem{T}}) where {T <: RingElem} = T <: FieldElem

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# TODO: what about polynomials over `Rational{BigInt}`?

@doc raw"""
var(a::PolyRing)
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31 changes: 30 additions & 1 deletion src/Rings.jl
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Expand Up @@ -95,12 +95,41 @@

# Type can only represent elements of an exact ring
# true unless explicitly specified
#
# implementors should only implement this trait for RingElem subtypes, but for
# convenience we support calling this also on Ring subtypes as well as Ring
# and RingElem instances
is_exact_type(R::Type{T}) where T <: RingElem = true

# Type can only represent elements of domains
is_exact_type(x) = is_exact_type(typeof(x))
is_exact_type(x::Type{<:Ring}) = is_exact_type(elem_type(x))
is_exact_type(T::DataType) = throw(MethodError(is_exact_type, (T,)))

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# Type can only represent elements of domains, i.e. without zero divisors
# false unless explicitly specified
#
# implementors should only implement this trait for RingElem subtypes, but for
# convenience we support calling this also on Ring subtypes as well as Ring
# and RingElem instances
is_domain_type(R::Type{T}) where T <: RingElem = false

is_domain_type(x) = is_domain_type(typeof(x))
is_domain_type(x::Type{<:Ring}) = is_domain_type(elem_type(x))
is_domain_type(T::DataType) = throw(MethodError(is_domain_type, (T,)))

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# Type can only represent elements of euclidean rings (which do not need to be domains)
# false unless explicitly specified
#
# implementors should only implement this trait for RingElem subtypes, but for
# convenience we support calling this also on Ring subtypes as well as Ring
# and RingElem instances
is_euclidean_type(R::Type{T}) where T <: RingElem = false

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is_euclidean_type(x) = is_euclidean_type(typeof(x))
is_euclidean_type(x::Type{<:Ring}) = is_euclidean_type(elem_type(x))
is_euclidean_type(T::DataType) = throw(MethodError(is_euclidean_type, (T,)))

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###############################################################################
#
# Exponential function for generic rings
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