test: old sq,adj,op = the graded Adj for SL/SAut

src/gradings.jl

@@ -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

src/roots.jl

@@ -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)
+function Base.show(io::IO, r::Root)
-⟂(α::AbstractRoot, β::AbstractRoot) = isorthogonal(α, β)
-
-function Base.show(io::IO, r::Root{N}) where {N}
     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) = Root(ntuple(k -> k == i ? 1 : 0, N))
-𝕖(N, i) = E(N, i)
 𝕆(N, ::Type{T}) where {T} = Root(ntuple(_ -> zero(T), N))
 
 """

test/graded_adj.jl

@@ -1,7 +1,53 @@
-@testset "Adj for SpN via grading" begin
+@testset "Adj via grading" begin
 
+    @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)
+
+        Δ = RSL(length(S)) - sum(RSL(s) for s in S)
+
+        Δs = let ψ = identity
+            PropertyT.laplacians(
+                RSL,
+                S,
+                x -> (gx = PropertyT.grading(ψ(x)); Set([gx, -gx])),
+            )
+        end
+
+        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 = 2
+        halfradius = 1
 
         SpN = MatrixGroups.SymplecticGroup{2genus}(Int8)
 
@@ -35,6 +81,6 @@
             end
             @test sum(PropertyT.Adj(Δs, subtype) for subtype in all_subtypes) == Δ^2
         end
-
+    end
 end