test: old sq,adj,op = the graded Adj for SL/SAut
This commit is contained in:
parent
b2b08e68c1
commit
4e93e78a9b
|
|
@ -25,7 +25,6 @@ end
|
|||
|
||||
grading(s::MatrixGroups.ElementarySymplectic) = Roots.Root(s)
|
||||
grading(e::MatrixGroups.ElementaryMatrix) = Roots.Root(e)
|
||||
grading(t::Groups.Transvection) = grading(Groups._abelianize(t))
|
||||
|
||||
function grading(g::FPGroupElement)
|
||||
if length(word(g)) == 1
|
||||
|
|
|
|||
|
|
@ -60,10 +60,7 @@ function positive(roots::AbstractVector{<:Root{N}}) where {N}
|
|||
return filter(α -> dot(α, pd) > 0.0, roots)
|
||||
end
|
||||
|
||||
Base.:~(α::AbstractRoot, β::AbstractRoot) = isproportional(α, β)
|
||||
⟂(α::AbstractRoot, β::AbstractRoot) = isorthogonal(α, β)
|
||||
|
||||
function Base.show(io::IO, r::Root{N}) where {N}
|
||||
function Base.show(io::IO, r::Root)
|
||||
print(io, "Root$(r.coord)")
|
||||
end
|
||||
|
||||
|
|
@ -73,8 +70,7 @@ function Base.show(io::IO, ::MIME"text/plain", r::Root{N}) where {N}
|
|||
print(io, "Root in ℝ^$N of length $l\n", r.coord)
|
||||
end
|
||||
|
||||
E(N, i::Integer) = Root(ntuple(k -> k == i ? 1 : 0, N))
|
||||
𝕖(N, i) = E(N, i)
|
||||
𝕖(N, i) = Root(ntuple(k -> k == i ? 1 : 0, N))
|
||||
𝕆(N, ::Type{T}) where {T} = Root(ntuple(_ -> zero(T), N))
|
||||
|
||||
"""
|
||||
|
|
|
|||
|
|
@ -1,40 +1,86 @@
|
|||
@testset "Adj for SpN via grading" begin
|
||||
@testset "Adj via grading" begin
|
||||
|
||||
genus = 3
|
||||
halfradius = 2
|
||||
@testset "SL(n,Z) & Aut(F₄)" begin
|
||||
n = 4
|
||||
halfradius = 1
|
||||
SL = MatrixGroups.SpecialLinearGroup{n}(Int8)
|
||||
RSL, S, sizes = PropertyT.group_algebra(SL, halfradius=halfradius, twisted=true)
|
||||
|
||||
SpN = MatrixGroups.SymplecticGroup{2genus}(Int8)
|
||||
Δ = RSL(length(S)) - sum(RSL(s) for s in S)
|
||||
|
||||
RSpN, S_sp, sizes_sp = PropertyT.group_algebra(SpN, halfradius=halfradius, twisted=true)
|
||||
|
||||
Δ, Δs = let RG = RSpN, S = S_sp, ψ = identity
|
||||
Δ = RG(length(S)) - sum(RG(s) for s in S)
|
||||
Δs = PropertyT.laplacians(
|
||||
RG,
|
||||
S,
|
||||
x -> (gx = PropertyT.grading(ψ(x)); Set([gx, -gx])),
|
||||
)
|
||||
Δ, Δs
|
||||
end
|
||||
|
||||
@testset "Adj correctness: genus=$genus" begin
|
||||
|
||||
all_subtypes = (
|
||||
:A₁, :C₁, Symbol("A₁×A₁"), Symbol("C₁×C₁"), Symbol("A₁×C₁"), :A₂, :C₂
|
||||
)
|
||||
|
||||
@test PropertyT.Adj(Δs, :A₂)[one(SpN)] == 384
|
||||
@test iszero(PropertyT.Adj(Δs, Symbol("A₁×A₁")))
|
||||
@test iszero(PropertyT.Adj(Δs, Symbol("C₁×C₁")))
|
||||
|
||||
@testset "divisibility by 16" begin
|
||||
for subtype in all_subtypes
|
||||
subtype in (:A₁, :C₁) && continue
|
||||
@test isinteger(PropertyT.Adj(Δs, subtype)[one(SpN)] / 16)
|
||||
end
|
||||
Δs = let ψ = identity
|
||||
PropertyT.laplacians(
|
||||
RSL,
|
||||
S,
|
||||
x -> (gx = PropertyT.grading(ψ(x)); Set([gx, -gx])),
|
||||
)
|
||||
end
|
||||
@test sum(PropertyT.Adj(Δs, subtype) for subtype in all_subtypes) == Δ^2
|
||||
|
||||
sq, adj, op = PropertyT.SqAdjOp(RSL, n)
|
||||
|
||||
@test PropertyT.Adj(Δs, :A₁) == sq
|
||||
@test PropertyT.Adj(Δs, :A₂) == adj
|
||||
@test PropertyT.Adj(Δs, Symbol("A₁×A₁")) == op
|
||||
|
||||
|
||||
halfradius = 1
|
||||
G = SpecialAutomorphismGroup(FreeGroup(n))
|
||||
RG, S, sizes = PropertyT.group_algebra(G, halfradius=halfradius, twisted=true)
|
||||
|
||||
Δ = RG(length(S)) - sum(RG(s) for s in S)
|
||||
|
||||
Δs = let ψ = Groups.Homomorphism(Groups._abelianize, G, SL)
|
||||
PropertyT.laplacians(
|
||||
RG,
|
||||
S,
|
||||
x -> (gx = PropertyT.grading(ψ(x)); Set([gx, -gx])),
|
||||
)
|
||||
end
|
||||
|
||||
sq, adj, op = PropertyT.SqAdjOp(RG, n)
|
||||
|
||||
@test PropertyT.Adj(Δs, :A₁) == sq
|
||||
@test PropertyT.Adj(Δs, :A₂) == adj
|
||||
@test PropertyT.Adj(Δs, Symbol("A₁×A₁")) == op
|
||||
end
|
||||
|
||||
|
||||
@testset "Symplectic group" begin
|
||||
genus = 3
|
||||
halfradius = 1
|
||||
|
||||
SpN = MatrixGroups.SymplecticGroup{2genus}(Int8)
|
||||
|
||||
RSpN, S_sp, sizes_sp = PropertyT.group_algebra(SpN, halfradius=halfradius, twisted=true)
|
||||
|
||||
Δ, Δs = let RG = RSpN, S = S_sp, ψ = identity
|
||||
Δ = RG(length(S)) - sum(RG(s) for s in S)
|
||||
Δs = PropertyT.laplacians(
|
||||
RG,
|
||||
S,
|
||||
x -> (gx = PropertyT.grading(ψ(x)); Set([gx, -gx])),
|
||||
)
|
||||
Δ, Δs
|
||||
end
|
||||
|
||||
@testset "Adj correctness: genus=$genus" begin
|
||||
|
||||
all_subtypes = (
|
||||
:A₁, :C₁, Symbol("A₁×A₁"), Symbol("C₁×C₁"), Symbol("A₁×C₁"), :A₂, :C₂
|
||||
)
|
||||
|
||||
@test PropertyT.Adj(Δs, :A₂)[one(SpN)] == 384
|
||||
@test iszero(PropertyT.Adj(Δs, Symbol("A₁×A₁")))
|
||||
@test iszero(PropertyT.Adj(Δs, Symbol("C₁×C₁")))
|
||||
|
||||
@testset "divisibility by 16" begin
|
||||
for subtype in all_subtypes
|
||||
subtype in (:A₁, :C₁) && continue
|
||||
@test isinteger(PropertyT.Adj(Δs, subtype)[one(SpN)] / 16)
|
||||
end
|
||||
end
|
||||
@test sum(PropertyT.Adj(Δs, subtype) for subtype in all_subtypes) == Δ^2
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
|
|
|
|||
Loading…
Reference in New Issue