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LocalizedEuclideanRing: add tests, fix some bugs, run conformance tests #2254

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660ff39
Add test for LocalizedEuclideanRing
fingolfin Dec 15, 2025
e249d38
Add characteristic(::LocalizedEuclideanRing)
fingolfin Dec 15, 2025
53510f1
Fix is_unit for LocalizedEuclideanRingElem
fingolfin Dec 15, 2025
6a7dc83
Use data(::LocalizedEuclideanRingElem) some more
fingolfin Dec 15, 2025
3d2c79c
Run conformance tests on LocalizedEuclideanRing
fingolfin Dec 15, 2025
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44 changes: 29 additions & 15 deletions src/generic/Misc/Localization.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -113,6 +113,8 @@ base_ring(L::LocalizedEuclideanRing) = L.base_ring::base_ring_type(L)

parent(a::LocalizedEuclideanRingElem) = a.parent

characteristic(L::LocalizedEuclideanRing) = characteristic(base_ring(L))

###############################################################################
#
# Basic manipulation
Expand All @@ -136,7 +138,8 @@ iszero(a::LocalizedEuclideanRingElem) = iszero(data(a))
isone(a::LocalizedEuclideanRingElem) = isone(data(a))

function is_unit(a::LocalizedEuclideanRingElem{T}) where {T <: RingElem}
return isin(inv(a.data), parent(a))
is_unit(data(a)) || return false
return isin(inv(data(a)), parent(a))
end

deepcopy_internal(a::LocalizedEuclideanRingElem, dict::IdDict) = parent(a)(deepcopy_internal(data(a), dict))
Expand Down Expand Up @@ -221,7 +224,7 @@ If 'checked = false' the invertibility of $a$ is not checked and the correspondi
of the Fraction Field is returned.
"""
function Base.inv(a::LocalizedEuclideanRingElem{T}, checked::Bool = true) where {T}
b = inv(a.data)
b = inv(data(a))
checked && (isin(b, parent(a)) || error("no unit"))
return LocalizedEuclideanRingElem{T}(b, parent(a), false)
end
Expand Down Expand Up @@ -255,8 +258,8 @@ function Base.divrem(a::LocalizedEuclideanRingElem{T}, b::LocalizedEuclideanRing
check_parent(a, b)
L = parent(a)
if L.comp
a1, s1 = ppio(numerator(a.data), L.prime)
a2, s2 = ppio(numerator(b.data), L.prime)
a1, s1 = ppio(numerator(data(a)), L.prime)
a2, s2 = ppio(numerator(data(b)), L.prime)
b1 = denominator(a)
b2 = denominator(b)
q, r = divrem(a1 * s1 * b2, s2)
Expand All @@ -274,9 +277,9 @@ end
function euclid(a::LocalizedEuclideanRingElem{T}) where {T <: RingElem}
L = parent(a)
if L.comp
return ppio(numerator(a.data), L.prime)[1]
return ppio(numerator(data(a)), L.prime)[1]
else
return ppio(numerator(a.data), L.prime)[2]
return ppio(numerator(data(a)), L.prime)[2]
end
end

Expand All @@ -292,9 +295,9 @@ function gcd(a::LocalizedEuclideanRingElem{T}, b::LocalizedEuclideanRingElem{T})
iszero(b) && return inv(canonical_unit(a)) * a
par = parent(a)
if par.comp
elem = ppio(gcd(numerator(a.data), numerator(b.data)), parent(a).prime)[2]
elem = ppio(gcd(numerator(data(a)), numerator(data(b))), parent(a).prime)[2]
else
elem = ppio(gcd(numerator(a.data), numerator(b.data)), parent(a).prime)[1]
elem = ppio(gcd(numerator(data(a)), numerator(data(b))), parent(a).prime)[1]
end
return par(elem)
end
Expand All @@ -304,9 +307,9 @@ function lcm(a::LocalizedEuclideanRingElem{T}, b::LocalizedEuclideanRingElem{T})
par = parent(a)
(iszero(a) || iszero(b)) && return par()
if par.comp
elem = ppio(lcm(numerator(a.data), numerator(b.data)), parent(a).prime)[2]
elem = ppio(lcm(numerator(data(a)), numerator(data(b))), parent(a).prime)[2]
else
elem = ppio(lcm(numerator(a.data), numerator(b.data)), parent(a).prime)[1]
elem = ppio(lcm(numerator(data(a)), numerator(data(b))), parent(a).prime)[1]
end
return par(elem)
end
Expand All @@ -320,9 +323,9 @@ end
function gcdx(a::LocalizedEuclideanRingElem{T}, b::LocalizedEuclideanRingElem{T}) where {T <: RingElement}
check_parent(a,b)
L = parent(a)
g, u, v = gcdx(numerator(a.data), numerator(b.data))
g, u, v = gcdx(numerator(data(a)), numerator(data(b)))
c = inv(canonical_unit(L(g)))
return c*L(g), c*L(u*denominator(a.data)), c*L(v*denominator(b.data))
return c*L(g), c*L(u*denominator(data(a))), c*L(v*denominator(data(b)))
end

###############################################################################
Expand All @@ -335,6 +338,17 @@ function ^(a::LocalizedEuclideanRingElem, b::Int)
return parent(a)(data(a)^b)
end

###############################################################################
#
# Conformance test element generation
#
###############################################################################

function ConformanceTests.generate_element(R::LocalizedEuclideanRing)
# TODO: should sometimes create something with a denominator
return R(ConformanceTests.generate_element(base_ring(R)))
end

###############################################################################
#
# Promotion rules
Expand Down Expand Up @@ -398,11 +412,11 @@ Returns unit `b`::LocalizedEuclideanRingElem{T} s.th. $a$ * `b` only consists of
"""
function canonical_unit(a::LocalizedEuclideanRingElem{T}) where {T <: RingElem}
if parent(a).comp
b = ppio(numerator(a.data), parent(a).prime)[1]
b = ppio(numerator(data(a)), parent(a).prime)[1]
else
b = ppio(numerator(a.data), parent(a).prime)[2]
b = ppio(numerator(data(a)), parent(a).prime)[2]
end
return parent(a)(b//denominator(a.data))
return parent(a)(b//denominator(data(a)))
end

###############################################################################
Expand Down
1 change: 1 addition & 0 deletions test/Rings-test.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -29,6 +29,7 @@ include("generic/Matrix-test.jl")
include("generic/MPoly-test.jl")
include("generic/LaurentMPoly-test.jl")
include("generic/UnivPoly-test.jl")
include("generic/Localization-test.jl")
include("algorithms/MPolyEvaluate-test.jl")
include("algorithms/MPolyFactor-test.jl")
include("algorithms/MPolyNested-test.jl")
Expand Down
138 changes: 138 additions & 0 deletions test/generic/Localization-test.jl
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Original file line number Diff line number Diff line change
@@ -0,0 +1,138 @@
@testset "Localization" begin

Qx, x = QQ["x"]

@testset "Conformance" begin
L = localization(Qx, x^2 + 1)
ConformanceTests.test_Ring_interface(L)
end

@testset "Constructor" begin

@test parent_type(LocalizedEuclideanRingElem{elem_type(Qx)}) == LocalizedEuclideanRing{elem_type(Qx)}

L = localization(Qx, x^2 + 1)
@test elem_type(L) == LocalizedEuclideanRingElem{elem_type(Qx)}
@test base_ring(L) == Qx
@test base_ring(L()) == Qx

L = localization(Qx, 4 * x^2 + x + 1)
@test elem_type(L) == LocalizedEuclideanRingElem{elem_type(Qx)}
@test base_ring(L) == Qx
@test base_ring(L()) == Qx

L = localization(Qx, [3 * x^4 + x + 18, x^9 + 3])
@test elem_type(L) == LocalizedEuclideanRingElem{elem_type(Qx)}
@test base_ring(L) == Qx
@test base_ring(L()) == Qx
end

@testset "Canonicalisation" begin

L = localization(Qx, 5x^2 + 3x + 2)
@test canonical_unit(L(5x^2 + 3x + 2)) == L(5)
@test canonical_unit(L(28)) == L(28)
@test canonical_unit(L(5 * x^4 + 3 * x^3 + 12 * x^2 + 6 * x + 4)) == L(5 * (x^2 + 2))

L = localization(Qx, [5x^2 + 3x + 2, x^16 + x + 3])
@test canonical_unit(L(x^16 + x + 3)) == one(L)
@test canonical_unit(L(89)) == L(89)
@test canonical_unit(L((5 * x^4 + 3 * x^3 + 12 * x^2 + 6 * x + 4) // (x^3 + 9))) == inv(L((1 // 5 * x^3 + 9 // 5) // (x^2 + 2)))
end

@testset "Parent object call overloading" begin

L1 = localization(Qx, 5x^2 + 3x + 2)
L2 = localization(Qx, 7x^3 + 2)
@test_throws ErrorException L1(L2(5))
@test parent(L1(4x // 7)) == L1

L = localization(Qx, [x^2 + 2, 3x^3 + 5])
@test parent(L(3x^2 + 6)) == L
@test_throws ErrorException L(15 // (3x^2 + 6))
@test_throws ErrorException L(17 // (9 * x^5 + 18 * x^3 + 15 * x^2 + 30))
@test_throws ErrorException L(19 // (9 * x^6 + 54 * x^5 + 18 * x^4 + 123 * x^3 + 90 * x^2 + 30 * x + 180))
end

@testset "GCDX" begin

L = localization(Qx, x^6 + 108)
a = L(x^10 + 2 * x^8 + 14 * x^7 + 49 * x^5 + 42 * x^3 + 294 * x^2 + 588)
b = L(x^11 + 14 * x^8 + 21 * x^6 + 294 * x^3 + 6)
(g, u, v) = gcdx(a, b)
@test g == u * a + v * b

L = localization(Qx, [x^6 + 108, x^8 + 12x^3 + 3])
a = L(x^10 + 2 * x^8 + 14 * x^7 + 49 * x^5 + 42 * x^3 + 294 * x^2 + 588)
b = L(x^11 + 14 * x^8 + 21 * x^6 + 294 * x^3 + 6)
(g, u, v) = gcdx(a, b)
@test g == u * a + v * b
end

@testset "GCD and LCM" begin

L = localization(Qx, x^6 + 108)
a = L(x^10 + 2 * x^8 + 14 * x^7 + 49 * x^5 + 42 * x^3 + 294 * x^2 + 588)
b = L(x^11 + 14 * x^8 + 21 * x^6 + 294 * x^3 + 6)
g = gcd(a, b)
@test g == L(1)
a = L(x^16 + 2 * x^14 + 14 * x^13 + 49 * x^11 + 108 * x^10 + 42 * x^9 + 510 * x^8 + 1512 * x^7 + 588 * x^6 + 5292 * x^5 + 4536 * x^3 + 31752 * x^2 + 63504)
b = L(x^17 + 14 * x^14 + 21 * x^12 + 108 * x^11 + 294 * x^9 + 1512 * x^8 + 2274 * x^6 + 31752 * x^3 + 648)
g = gcd(a, b)
@test g == L(x^6 + 108)

L = localization(Qx, [x^6 + 108, x^8 + 12x^3 + 3])
a = L(x^10 + 2 * x^8 + 14 * x^7 + 49 * x^5 + 42 * x^3 + 294 * x^2 + 588)
b = L(x^13 + 2 * x^11 + 14 * x^10 + 49 * x^8 + 42 * x^6 + 294 * x^5 + 588 * x^3 + 6 * x^2 + 12)
g = gcd(a, b)
@test g == L(1)
end

@testset "Exact division" begin
L = localization(Qx, x^6 + 108)
@test_throws ErrorException divexact(L(9), L(2x^6 + 216))
a = L(x^10 + 2 * x^8 + 14 * x^7 + 49 * x^5 + 42 * x^3 + 294 * x^2 + 588)
b = L(x^11 + 14 * x^8 + 21 * x^6 + 294 * x^3 + 6)
g = divides(a, b)
@test a == b * g[2]
@test g[1] == true
a = L(x^16 + 2 * x^14 + 14 * x^13 + 49 * x^11 + 108 * x^10 + 42 * x^9 + 510 * x^8 + 1512 * x^7 + 588 * x^6 + 5292 * x^5 + 4536 * x^3 + 31752 * x^2 + 63504)
b = L(x^17 + 14 * x^14 + 21 * x^12 + 108 * x^11 + 294 * x^9 + 1512 * x^8 + 2274 * x^6 + 31752 * x^3 + 648)
@test a == b * g[2]
@test g[1] == true
end

@testset "Inversion" begin
L = localization(Qx, x^6 + 108)
@test_throws ErrorException inv(L(2x^6 + 216))
@test inv(L(x^2 + 108)) == L(1 // (x^2 + 108))

L = localization(Qx, [x^6 + 3, x^3 + 5])
@test_throws ErrorException inv(L(2x^6 + 6))
@test inv(L(x^2 + 108)) == L(1 // (x^2 + 108))
end

@testset "Binary operators" begin
L = localization(Qx, x^6 + 108)
@test L(18x // 2) + L(2x // 1) == L(11x)
@test L(18x // 3) - L(1x) == L(5x)
@test L(32x) * L(4x) == L(128x^2)

L = localization(Qx, [x^6 + 3, x^3 + 5])
@test L(18x // 2) + L(2x // 1) == L(11x)
@test L(18x // 3) - L(1x) == L(5x)
@test L(32x) * L(4x) == L(128x^2)
end

@testset "Basic manipulation" begin
L = localization(Qx, x^6 + 108)
@test iszero(L(x^2 + x)) == false
@test isone(L(x^2 // x^2)) == true
@test is_unit(L(x)) == true

L = localization(Qx, [x^6 + 3, x^3 + 5])
@test iszero(L(x - x)) == true
@test isone(L(x^2 + 3x)) == false
@test is_unit(L((x^3 + 5) // (x^3 + 5)))
end
end
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