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Adapt tests
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@lgoettgens
lgoettgens committed Nov 25, 2024
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Showing 1 changed file with 132 additions and 105 deletions.
237 changes: 132 additions & 105 deletions experimental/LieAlgebras/test/LieAlgebraModule-test.jl
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Expand Up @@ -780,138 +780,155 @@
end

@testset "dominant_character" begin
is_dominant_weight = Oscar.LieAlgebras.is_dominant_weight

function check_dominant_character(
LR::Union{LieAlgebra,RootSystem}, hw::Vector{<:Oscar.IntegerUnion}
)
domchar = @inferred dominant_character(LR, hw)
@test domchar[Int.(hw)] == 1
@test issetequal(keys(domchar), dominant_weights(Vector{Int}, LR, hw))
@test all(is_dominant_weight, keys(domchar))
R = LR isa RootSystem ? LR : root_system(LR)
@test domchar isa Dict{WeightLatticeElem,Int}
@test domchar[WeightLatticeElem(R, hw)] == 1
@test issetequal(keys(domchar), dominant_weights(LR, hw))
@test all(is_dominant, keys(domchar))
@test all(>=(1), values(domchar))

domchar_ZZ = @inferred dominant_character(ZZRingElem, LR, hw)
@test domchar_ZZ isa Dict{WeightLatticeElem,ZZRingElem}
@test domchar_ZZ == Dict{WeightLatticeElem,ZZRingElem}(domchar)

return domchar
end

# All concrete test results have been computed using the LiE CAS (http://wwwmathlabo.univ-poitiers.fr/~maavl/LiE/) v2.2.2
let R = root_system(Tuple{Symbol,Int}[]), hw = Int[]
domchar = check_dominant_character(R, hw)
@test domchar == Dict(Int[] => 1)
@test domchar == Dict(WeightLatticeElem(R, Int[]) => 1)
end

let L = lie_algebra(QQ, :A, 2), hw = [0, 0]
domchar = check_dominant_character(L, hw)
@test domchar == Dict([0, 0] => 1)
R = root_system(L)
@test domchar == Dict(WeightLatticeElem(R, [0, 0]) => 1)
end

let L = lie_algebra(QQ, :A, 3), hw = ZZ.([1, 1, 1])
domchar = check_dominant_character(L, hw)
@test domchar == Dict([1, 1, 1] => 1, [2, 0, 0] => 2, [0, 0, 2] => 2, [0, 1, 0] => 4)
R = root_system(L)
@test domchar == Dict(
WeightLatticeElem(R, [1, 1, 1]) => 1,
WeightLatticeElem(R, [2, 0, 0]) => 2,
WeightLatticeElem(R, [0, 0, 2]) => 2,
WeightLatticeElem(R, [0, 1, 0]) => 4,
)
end

let L = lie_algebra(QQ, :C, 3), hw = [2, 0, 1]
domchar = check_dominant_character(L, hw)
R = root_system(L)
@test domchar == Dict(
[2, 0, 1] => 1,
[0, 1, 1] => 1,
[3, 0, 0] => 1,
[1, 1, 0] => 3,
[0, 0, 1] => 6,
[1, 0, 0] => 7,
WeightLatticeElem(R, [2, 0, 1]) => 1,
WeightLatticeElem(R, [0, 1, 1]) => 1,
WeightLatticeElem(R, [3, 0, 0]) => 1,
WeightLatticeElem(R, [1, 1, 0]) => 3,
WeightLatticeElem(R, [0, 0, 1]) => 6,
WeightLatticeElem(R, [1, 0, 0]) => 7,
)
end

let L = lie_algebra(QQ, :D, 4), hw = [0, 3, 1, 0]
domchar = check_dominant_character(L, hw)
R = root_system(L)
@test domchar == Dict(
[0, 3, 1, 0] => 1,
[1, 1, 2, 1] => 1,
[1, 2, 0, 1] => 2,
[2, 0, 3, 0] => 1,
[2, 0, 1, 2] => 2,
[0, 0, 3, 2] => 1,
[2, 1, 1, 0] => 3,
[0, 1, 3, 0] => 2,
[0, 1, 1, 2] => 3,
[0, 2, 1, 0] => 7,
[3, 0, 0, 1] => 4,
[1, 0, 2, 1] => 8,
[1, 0, 0, 3] => 4,
[1, 1, 0, 1] => 12,
[2, 0, 1, 0] => 16,
[0, 0, 3, 0] => 12,
[0, 0, 1, 2] => 16,
[0, 1, 1, 0] => 26,
[1, 0, 0, 1] => 36,
[0, 0, 1, 0] => 56,
WeightLatticeElem(R, [0, 3, 1, 0]) => 1,
WeightLatticeElem(R, [1, 1, 2, 1]) => 1,
WeightLatticeElem(R, [1, 2, 0, 1]) => 2,
WeightLatticeElem(R, [2, 0, 3, 0]) => 1,
WeightLatticeElem(R, [2, 0, 1, 2]) => 2,
WeightLatticeElem(R, [0, 0, 3, 2]) => 1,
WeightLatticeElem(R, [2, 1, 1, 0]) => 3,
WeightLatticeElem(R, [0, 1, 3, 0]) => 2,
WeightLatticeElem(R, [0, 1, 1, 2]) => 3,
WeightLatticeElem(R, [0, 2, 1, 0]) => 7,
WeightLatticeElem(R, [3, 0, 0, 1]) => 4,
WeightLatticeElem(R, [1, 0, 2, 1]) => 8,
WeightLatticeElem(R, [1, 0, 0, 3]) => 4,
WeightLatticeElem(R, [1, 1, 0, 1]) => 12,
WeightLatticeElem(R, [2, 0, 1, 0]) => 16,
WeightLatticeElem(R, [0, 0, 3, 0]) => 12,
WeightLatticeElem(R, [0, 0, 1, 2]) => 16,
WeightLatticeElem(R, [0, 1, 1, 0]) => 26,
WeightLatticeElem(R, [1, 0, 0, 1]) => 36,
WeightLatticeElem(R, [0, 0, 1, 0]) => 56,
)
end

let R = root_system(:E, 6), hw = [1, 0, 1, 0, 1, 0]
domchar = check_dominant_character(R, hw)
@test domchar == Dict(
[1, 0, 1, 0, 1, 0] => 1,
[0, 0, 0, 1, 1, 0] => 2,
[2, 1, 0, 0, 0, 1] => 3,
[0, 1, 1, 0, 0, 1] => 6,
[2, 0, 1, 0, 0, 0] => 10,
[1, 0, 0, 0, 1, 1] => 16,
[1, 2, 0, 0, 0, 0] => 15,
[0, 0, 2, 0, 0, 0] => 20,
[1, 0, 0, 1, 0, 0] => 44,
[0, 1, 0, 0, 0, 2] => 36,
[0, 1, 0, 0, 1, 0] => 92,
[2, 0, 0, 0, 0, 1] => 104,
[0, 0, 1, 0, 0, 1] => 204,
[1, 1, 0, 0, 0, 0] => 425,
[0, 0, 0, 0, 0, 2] => 416,
[0, 0, 0, 0, 1, 0] => 836,
[1, 0, 0, 0, 0, 0] => 1600,
WeightLatticeElem(R, [1, 0, 1, 0, 1, 0]) => 1,
WeightLatticeElem(R, [0, 0, 0, 1, 1, 0]) => 2,
WeightLatticeElem(R, [2, 1, 0, 0, 0, 1]) => 3,
WeightLatticeElem(R, [0, 1, 1, 0, 0, 1]) => 6,
WeightLatticeElem(R, [2, 0, 1, 0, 0, 0]) => 10,
WeightLatticeElem(R, [1, 0, 0, 0, 1, 1]) => 16,
WeightLatticeElem(R, [1, 2, 0, 0, 0, 0]) => 15,
WeightLatticeElem(R, [0, 0, 2, 0, 0, 0]) => 20,
WeightLatticeElem(R, [1, 0, 0, 1, 0, 0]) => 44,
WeightLatticeElem(R, [0, 1, 0, 0, 0, 2]) => 36,
WeightLatticeElem(R, [0, 1, 0, 0, 1, 0]) => 92,
WeightLatticeElem(R, [2, 0, 0, 0, 0, 1]) => 104,
WeightLatticeElem(R, [0, 0, 1, 0, 0, 1]) => 204,
WeightLatticeElem(R, [1, 1, 0, 0, 0, 0]) => 425,
WeightLatticeElem(R, [0, 0, 0, 0, 0, 2]) => 416,
WeightLatticeElem(R, [0, 0, 0, 0, 1, 0]) => 836,
WeightLatticeElem(R, [1, 0, 0, 0, 0, 0]) => 1600,
)
end

let L = lie_algebra(QQ, :G, 2), hw = [1, 2]
domchar = check_dominant_character(L, hw)
R = root_system(L)
@test domchar == Dict(
[1, 2] => 1,
[4, 0] => 1,
[2, 1] => 2,
[0, 2] => 2,
[3, 0] => 3,
[1, 1] => 5,
[2, 0] => 7,
[0, 1] => 7,
[1, 0] => 10,
[0, 0] => 10,
WeightLatticeElem(R, [1, 2]) => 1,
WeightLatticeElem(R, [4, 0]) => 1,
WeightLatticeElem(R, [2, 1]) => 2,
WeightLatticeElem(R, [0, 2]) => 2,
WeightLatticeElem(R, [3, 0]) => 3,
WeightLatticeElem(R, [1, 1]) => 5,
WeightLatticeElem(R, [2, 0]) => 7,
WeightLatticeElem(R, [0, 1]) => 7,
WeightLatticeElem(R, [1, 0]) => 10,
WeightLatticeElem(R, [0, 0]) => 10,
)
end

let L = special_linear_lie_algebra(QQ, 2), hw = [7] # type A_1 but without known root system
domchar = check_dominant_character(L, hw)
R = root_system(L)
@test domchar == Dict(
[7] => 1,
[5] => 1,
[3] => 1,
[1] => 1,
WeightLatticeElem(R, [7]) => 1,
WeightLatticeElem(R, [5]) => 1,
WeightLatticeElem(R, [3]) => 1,
WeightLatticeElem(R, [1]) => 1,
)
end

let L = special_orthogonal_lie_algebra(QQ, 7), hw = ZZ.([1, 2, 0]) # type B_3 but without known root system
domchar = check_dominant_character(L, hw)
R = root_system(L)
@test domchar == Dict(
[1, 2, 0] => 1,
[2, 0, 2] => 1,
[2, 1, 0] => 1,
[0, 1, 2] => 2,
[0, 2, 0] => 2,
[3, 0, 0] => 2,
[1, 0, 2] => 3,
[1, 1, 0] => 6,
[2, 0, 0] => 6,
[0, 0, 2] => 9,
[0, 1, 0] => 9,
[1, 0, 0] => 15,
[0, 0, 0] => 15,
WeightLatticeElem(R, [1, 2, 0]) => 1,
WeightLatticeElem(R, [2, 0, 2]) => 1,
WeightLatticeElem(R, [2, 1, 0]) => 1,
WeightLatticeElem(R, [0, 1, 2]) => 2,
WeightLatticeElem(R, [0, 2, 0]) => 2,
WeightLatticeElem(R, [3, 0, 0]) => 2,
WeightLatticeElem(R, [1, 0, 2]) => 3,
WeightLatticeElem(R, [1, 1, 0]) => 6,
WeightLatticeElem(R, [2, 0, 0]) => 6,
WeightLatticeElem(R, [0, 0, 2]) => 9,
WeightLatticeElem(R, [0, 1, 0]) => 9,
WeightLatticeElem(R, [1, 0, 0]) => 15,
WeightLatticeElem(R, [0, 0, 0]) => 15,
)
end
end
Expand All @@ -921,44 +938,53 @@
LR::Union{LieAlgebra,RootSystem}, hw::Vector{<:Oscar.IntegerUnion}
)
char = @inferred character(LR, hw)
@test char[Int.(hw)] == 1
R = LR isa RootSystem ? LR : root_system(LR)
@test char isa Dict{WeightLatticeElem,Int}
@test char[WeightLatticeElem(R, hw)] == 1
@test all(>=(1), values(char))
@test sum(values(char)) == dim_of_simple_module(LR, hw)
domchar = @inferred dominant_character(LR, hw)
@test all(w -> domchar[w] == char[w], keys(domchar))

char_ZZ = @inferred character(ZZRingElem, LR, hw)
@test char_ZZ isa Dict{WeightLatticeElem,ZZRingElem}
@test char_ZZ == Dict{WeightLatticeElem,ZZRingElem}(char)

return char
end

# All concrete test results have been computed using the LiE CAS (http://wwwmathlabo.univ-poitiers.fr/~maavl/LiE/) v2.2.2
let R = root_system(Tuple{Symbol,Int}[]), hw = Int[]
domchar = check_character(R, hw)
@test domchar == Dict(Int[] => 1)
@test domchar == Dict(WeightLatticeElem(R, Int[]) => 1)
end

let L = lie_algebra(QQ, :A, 2), hw = [0, 0]
domchar = check_character(L, hw)
@test domchar == Dict([0, 0] => 1)
R = root_system(L)
@test domchar == Dict(WeightLatticeElem(R, [0, 0]) => 1)
end

let L = lie_algebra(QQ, :A, 3), hw = ZZ.([1, 1, 0])
char = check_character(L, hw)
R = root_system(L)
@test char == Dict(
[1, 1, 0] => 1,
[2, -1, 1] => 1,
[-1, 2, 0] => 1,
[2, 0, -1] => 1,
[0, 0, 1] => 2,
[1, -2, 2] => 1,
[0, 1, -1] => 2,
[-2, 1, 1] => 1,
[1, -1, 0] => 2,
[-1, -1, 2] => 1,
[-2, 2, -1] => 1,
[1, 0, -2] => 1,
[-1, 0, 0] => 2,
[0, -2, 1] => 1,
[-1, 1, -2] => 1,
[0, -1, -1] => 1,
WeightLatticeElem(R, [1, 1, 0]) => 1,
WeightLatticeElem(R, [2, -1, 1]) => 1,
WeightLatticeElem(R, [-1, 2, 0]) => 1,
WeightLatticeElem(R, [2, 0, -1]) => 1,
WeightLatticeElem(R, [0, 0, 1]) => 2,
WeightLatticeElem(R, [1, -2, 2]) => 1,
WeightLatticeElem(R, [0, 1, -1]) => 2,
WeightLatticeElem(R, [-2, 1, 1]) => 1,
WeightLatticeElem(R, [1, -1, 0]) => 2,
WeightLatticeElem(R, [-1, -1, 2]) => 1,
WeightLatticeElem(R, [-2, 2, -1]) => 1,
WeightLatticeElem(R, [1, 0, -2]) => 1,
WeightLatticeElem(R, [-1, 0, 0]) => 2,
WeightLatticeElem(R, [0, -2, 1]) => 1,
WeightLatticeElem(R, [-1, 1, -2]) => 1,
WeightLatticeElem(R, [0, -1, -1]) => 1,
)
end

Expand All @@ -980,15 +1006,16 @@

let L = special_linear_lie_algebra(QQ, 2), hw = [7] # type A_1 but without known root system
char = check_character(L, hw)
R = root_system(L)
@test char == Dict(
[7] => 1,
[5] => 1,
[3] => 1,
[1] => 1,
[-1] => 1,
[-3] => 1,
[-5] => 1,
[-7] => 1,
WeightLatticeElem(R, [7]) => 1,
WeightLatticeElem(R, [5]) => 1,
WeightLatticeElem(R, [3]) => 1,
WeightLatticeElem(R, [1]) => 1,
WeightLatticeElem(R, [-1]) => 1,
WeightLatticeElem(R, [-3]) => 1,
WeightLatticeElem(R, [-5]) => 1,
WeightLatticeElem(R, [-7]) => 1,
)
end

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