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Tests for the specific example of Aut(F_4)
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@ -120,4 +120,30 @@ end
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@test a*b == b*a
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@test a*b == b*a
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@test a^3 * b^3 == one(a)
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@test a^3 * b^3 == one(a)
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end
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end
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@testset "specific Aut(𝔽₄) tests" begin
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N = 4
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import Combinatorics.nthperm
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SymmetricGroup(n) = [nthperm(collect(1:n), k) for k in 1:factorial(n)]
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indexing = [[i,j] for i in 1:N for j in 1:N if i≠j]
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σs = [symmetric_AutSymbol(perm) for perm in SymmetricGroup(N)[2:end]];
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ϱs = [rmul_AutSymbol(i,j) for (i,j) in indexing]
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λs = [lmul_AutSymbol(i,j) for (i,j) in indexing]
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ɛs = [flip_AutSymbol(i) for i in 1:N];
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S = vcat(ϱs, λs, σs, ɛs)
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S = vcat(S, [inv(s) for s in S])
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@test isa(S, Vector{AutSymbol})
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@test length(S) == 102
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@test length(unique(S)) == 75
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S₁ = [GWord(s) for s in unique(S)]
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@test isa(S₁, Vector{AutWord})
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p = prod(S₁)
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@test length(p) == 75
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@test Group.simplify_perms!(p) == false
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@test length(p) == 53
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@test Group.join_free_symbols!(p) == true
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end
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end
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end
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