From 7d95338e3302c9eed886406d2e5c2398765d1f44 Mon Sep 17 00:00:00 2001 From: kalmarek Date: Wed, 25 Mar 2020 05:25:02 +0100 Subject: [PATCH] fix tests --- test/AutGroup-tests.jl | 127 ++++++++++++++++++++-------------------- test/FPGroup-tests.jl | 13 ++-- test/FreeGroup-tests.jl | 39 ++++++------ 3 files changed, 87 insertions(+), 92 deletions(-) diff --git a/test/AutGroup-tests.jl b/test/AutGroup-tests.jl index 8a0c9b9..3d140d6 100644 --- a/test/AutGroup-tests.jl +++ b/test/AutGroup-tests.jl @@ -8,72 +8,73 @@ f = Groups.AutSymbol(:a, 1, Groups.FlipAut(2)) @test isa(f, Groups.GSymbol) @test isa(f, Groups.AutSymbol) - @test isa(Groups.perm_autsymbol(Int8.([1,2,3,4])), Groups.AutSymbol) - @test isa(Groups.rmul_autsymbol(1,2), Groups.AutSymbol) - @test isa(Groups.lmul_autsymbol(3,4), Groups.AutSymbol) - @test isa(Groups.flip_autsymbol(3), Groups.AutSymbol) + @test isa(Groups.AutSymbol(perm"(4)"), Groups.AutSymbol) + @test isa(Groups.AutSymbol([2,3,4,1]), Groups.AutSymbol) + @test isa(Groups.transvection_R(1,2), Groups.AutSymbol) + @test isa(Groups.transvection_R(3,4), Groups.AutSymbol) + @test isa(Groups.flip(3), Groups.AutSymbol) end a,b,c,d = gens(FreeGroup(4)) D = NTuple{4,FreeGroupElem}([a,b,c,d]) - @testset "flip_autsymbol correctness" begin - @test Groups.flip_autsymbol(1)(deepcopy(D)) == (a^-1, b,c,d) - @test Groups.flip_autsymbol(2)(deepcopy(D)) == (a, b^-1,c,d) - @test Groups.flip_autsymbol(3)(deepcopy(D)) == (a, b,c^-1,d) - @test Groups.flip_autsymbol(4)(deepcopy(D)) == (a, b,c,d^-1) - @test inv(Groups.flip_autsymbol(1))(deepcopy(D)) == (a^-1, b,c,d) - @test inv(Groups.flip_autsymbol(2))(deepcopy(D)) == (a, b^-1,c,d) - @test inv(Groups.flip_autsymbol(3))(deepcopy(D)) == (a, b,c^-1,d) - @test inv(Groups.flip_autsymbol(4))(deepcopy(D)) == (a, b,c,d^-1) + @testset "flip correctness" begin + @test Groups.flip(1)(deepcopy(D)) == (a^-1, b,c,d) + @test Groups.flip(2)(deepcopy(D)) == (a, b^-1,c,d) + @test Groups.flip(3)(deepcopy(D)) == (a, b,c^-1,d) + @test Groups.flip(4)(deepcopy(D)) == (a, b,c,d^-1) + @test inv(Groups.flip(1))(deepcopy(D)) == (a^-1, b,c,d) + @test inv(Groups.flip(2))(deepcopy(D)) == (a, b^-1,c,d) + @test inv(Groups.flip(3))(deepcopy(D)) == (a, b,c^-1,d) + @test inv(Groups.flip(4))(deepcopy(D)) == (a, b,c,d^-1) end - @testset "perm_autsymbol correctness" begin - σ = Groups.perm_autsymbol([1,2,3,4]) + @testset "perm correctness" begin + σ = Groups.AutSymbol(perm"(4)") @test σ(deepcopy(D)) == deepcopy(D) @test inv(σ)(deepcopy(D)) == deepcopy(D) - σ = Groups.perm_autsymbol([2,3,4,1]) + σ = Groups.AutSymbol(perm"(1,2,3,4)") @test σ(deepcopy(D)) == (b, c, d, a) @test inv(σ)(deepcopy(D)) == (d, a, b, c) - σ = Groups.perm_autsymbol([2,1,4,3]) + σ = Groups.AutSymbol(perm"(1,2)(4,3)") @test σ(deepcopy(D)) == (b, a, d, c) @test inv(σ)(deepcopy(D)) == (b, a, d, c) - σ = Groups.perm_autsymbol([2,3,1,4]) + σ = Groups.AutSymbol(perm"(1,2,3)(4)") @test σ(deepcopy(D)) == (b, c, a, d) @test inv(σ)(deepcopy(D)) == (c, a, b, d) end - @testset "rmul/lmul_autsymbol correctness" begin + @testset "rmul/transvection_R correctness" begin i,j = 1,2 - r = Groups.rmul_autsymbol(i,j) - l = Groups.lmul_autsymbol(i,j) + r = Groups.transvection_R(i,j) + l = Groups.transvection_L(i,j) @test r(deepcopy(D)) == (a*b, b, c, d) @test inv(r)(deepcopy(D)) == (a*b^-1,b, c, d) @test l(deepcopy(D)) == (b*a, b, c, d) @test inv(l)(deepcopy(D)) == (b^-1*a,b, c, d) i,j = 3,1 - r = Groups.rmul_autsymbol(i,j) - l = Groups.lmul_autsymbol(i,j) + r = Groups.transvection_R(i,j) + l = Groups.transvection_L(i,j) @test r(deepcopy(D)) == (a, b, c*a, d) @test inv(r)(deepcopy(D)) == (a, b, c*a^-1,d) @test l(deepcopy(D)) == (a, b, a*c, d) @test inv(l)(deepcopy(D)) == (a, b, a^-1*c,d) i,j = 4,3 - r = Groups.rmul_autsymbol(i,j) - l = Groups.lmul_autsymbol(i,j) + r = Groups.transvection_R(i,j) + l = Groups.transvection_L(i,j) @test r(deepcopy(D)) == (a, b, c, d*c) @test inv(r)(deepcopy(D)) == (a, b, c, d*c^-1) @test l(deepcopy(D)) == (a, b, c, c*d) @test inv(l)(deepcopy(D)) == (a, b, c, c^-1*d) i,j = 2,4 - r = Groups.rmul_autsymbol(i,j) - l = Groups.lmul_autsymbol(i,j) + r = Groups.transvection_R(i,j) + l = Groups.transvection_L(i,j) @test r(deepcopy(D)) == (a, b*d, c, d) @test inv(r)(deepcopy(D)) == (a, b*d^-1,c, d) @test l(deepcopy(D)) == (a, d*b, c, d) @@ -94,40 +95,40 @@ @test length(Groups.gens(A)) == 0 A = AutGroup(FreeGroup(2)) @test length(Groups.gens(A)) == 7 - gens = Groups.gens(A) + Agens = Groups.gens(A) - @test isa(A(Groups.rmul_autsymbol(1,2)), Automorphism) - @test A(Groups.rmul_autsymbol(1,2)) in gens + @test isa(A(Groups.transvection_R(1,2)), Automorphism) + @test A(Groups.transvection_R(1,2)) in Agens - @test isa(A(Groups.rmul_autsymbol(2,1)), Automorphism) - @test A(Groups.rmul_autsymbol(2,1)) in gens + @test isa(A(Groups.transvection_R(2,1)), Automorphism) + @test A(Groups.transvection_R(2,1)) in Agens - @test isa(A(Groups.lmul_autsymbol(1,2)), Automorphism) - @test A(Groups.lmul_autsymbol(1,2)) in gens + @test isa(A(Groups.transvection_R(1,2)), Automorphism) + @test A(Groups.transvection_R(1,2)) in Agens - @test isa(A(Groups.lmul_autsymbol(2,1)), Automorphism) - @test A(Groups.lmul_autsymbol(2,1)) in gens + @test isa(A(Groups.transvection_R(2,1)), Automorphism) + @test A(Groups.transvection_R(2,1)) in Agens - @test isa(A(Groups.flip_autsymbol(1)), Automorphism) - @test A(Groups.flip_autsymbol(1)) in gens + @test isa(A(Groups.flip(1)), Automorphism) + @test A(Groups.flip(1)) in Agens - @test isa(A(Groups.flip_autsymbol(2)), Automorphism) - @test A(Groups.flip_autsymbol(2)) in gens + @test isa(A(Groups.flip(2)), Automorphism) + @test A(Groups.flip(2)) in Agens - @test isa(A(Groups.perm_autsymbol([2,1])), Automorphism) - @test A(Groups.perm_autsymbol([2,1])) in gens + @test isa(A(Groups.AutSymbol(perm"(1,2)")), Automorphism) + @test A(Groups.AutSymbol(perm"(1,2)")) in Agens end A = AutGroup(FreeGroup(4)) @testset "eltary functions" begin - f = Groups.perm_autsymbol([2,3,4,1]) + f = Groups.AutSymbol(perm"(1,2,3,4)") @test (Groups.change_pow(f, 2)).pow == 1 @test (Groups.change_pow(f, -2)).pow == 1 @test (inv(f)).pow == 1 - f = Groups.perm_autsymbol([2,1,4,3]) + f = Groups.AutSymbol(perm"(1,2)(3,4)") @test isa(inv(f), Groups.AutSymbol) @test_throws MethodError f*f @@ -136,14 +137,15 @@ end @testset "reductions/arithmetic" begin - f = Groups.perm_autsymbol([2,3,4,1]) + f = Groups.AutSymbol(perm"(1,2,3,4)") - f² = Groups.r_multiply(A(f), [f], reduced=false) - @test Groups.simplifyperms!(f²) == false + f² = append!(A(f), [f]) + @test Groups.simplifyperms!(Bool, f²) == false @test f²^2 == one(A) + @test !isone(f²) - a = A(Groups.rmul_autsymbol(1,2))*Groups.flip_autsymbol(2) - b = Groups.flip_autsymbol(2)*A(inv(Groups.rmul_autsymbol(1,2))) + a = A(Groups.transvection_L(1,2))*Groups.flip(2) + b = Groups.flip(2)*A(inv(Groups.transvection_L(1,2))) @test a*b == b*a @test a^3 * b^3 == one(A) g,h = Groups.gens(A)[[1,8]] # (g, h) = (ϱ₁₂, ϱ₃₂) @@ -164,27 +166,22 @@ # Not so simple arithmetic: applying starting on the left: # ϱ₁₂*ϱ₂₁⁻¹*λ₁₂*ε₂ == σ₂₁₃₄ - g = A(Groups.rmul_autsymbol(1,2)) + g = A(Groups.transvection_R(1,2)) x1, x2, x3, x4 = Groups.domain(A) @test g(Groups.domain(A)) == (x1*x2, x2, x3, x4) - g = g*inv(A(Groups.rmul_autsymbol(2,1))) + g = g*inv(A(Groups.transvection_R(2,1))) @test g(Groups.domain(A)) == (x1*x2, x1^-1, x3, x4) - g = g*A(Groups.lmul_autsymbol(1,2)) + g = g*A(Groups.transvection_L(1,2)) @test g(Groups.domain(A)) == (x2, x1^-1, x3, x4) - g = g*A(Groups.flip_autsymbol(2)) + g = g*A(Groups.flip(2)) @test g(Groups.domain(A)) == (x2, x1, x3, x4) - @test g(Groups.domain(A)) == A(Groups.perm_autsymbol([2,1,3,4]))(Groups.domain(A)) + @test g(Groups.domain(A)) == A(Groups.AutSymbol(perm"(1,2)(4)"))(Groups.domain(A)) - @test g == A(Groups.perm_autsymbol([2,1,3,4])) + @test g == A(Groups.AutSymbol(perm"(1,2)(4)")) g_im = g(Groups.domain(A)) - @test length(g_im[1]) == 5 - @test length(g_im[2]) == 3 - @test length(g_im[3]) == 1 - @test length(g_im[4]) == 1 - @test length.(Groups.reduce!.(g_im)) == (1,1,1,1) - + @test length.(g_im) == (1,1,1,1) end @testset "specific Aut(F4) tests" begin @@ -219,8 +216,8 @@ M = Matrix{Int}(I, N, N) M[1,2] = 1 - ϱ₁₂ = G(Groups.rmul_autsymbol(1,2)) - λ₁₂ = G(Groups.rmul_autsymbol(1,2)) + ϱ₁₂ = G(Groups.transvection_R(1,2)) + λ₁₂ = G(Groups.transvection_R(1,2)) @test Groups.linear_repr(ϱ₁₂) == M @test Groups.linear_repr(λ₁₂) == M @@ -235,14 +232,14 @@ M = Matrix{Int}(I, N, N) M[2,2] = -1 - ε₂ = G(Groups.flip_autsymbol(2)) + ε₂ = G(Groups.flip(2)) @test Groups.linear_repr(ε₂) == M @test Groups.linear_repr(ε₂^2) == Matrix{Int}(I, N, N) M = [0 1 0; 0 0 1; 1 0 0] - σ = G(Groups.perm_autsymbol([2,3,1])) + σ = G(Groups.AutSymbol(perm"(1,2,3)")) @test Groups.linear_repr(σ) == M @test Groups.linear_repr(σ^3) == Matrix{Int}(I, 3, 3) @test Groups.linear_repr(σ)^3 == Matrix{Int}(I, 3, 3) diff --git a/test/FPGroup-tests.jl b/test/FPGroup-tests.jl index 831b78e..ddf29e9 100644 --- a/test/FPGroup-tests.jl +++ b/test/FPGroup-tests.jl @@ -1,15 +1,18 @@ @testset "FPGroups definitions" begin F = FreeGroup(["a", "b", "c"]) - a,b,c = gens(F) + a,b,c = Groups.gens(F) R = [a^2, a*b*a, c*b*a] @test F/R isa FPGroup @test F isa FreeGroup G = F/R - A,B,C = gens(G) + A,B,C = Groups.gens(G) - @test A^2 == one(G) - @test A*B*A*A == A - @test A*A*B*A == B*A + @test Groups.reduce!(A^2) == one(G) + @test Groups.reduce!(A*B*A*A) == A + @test Groups.reduce!(A*A*B*A) == A + + @test Groups.freepreimage(G) == F + @test Groups.freepreimage(B^2) == b^2 @test G/[B^2, C*B*C] isa FPGroup end diff --git a/test/FreeGroup-tests.jl b/test/FreeGroup-tests.jl index cd0df27..da39e75 100644 --- a/test/FreeGroup-tests.jl +++ b/test/FreeGroup-tests.jl @@ -55,23 +55,18 @@ end @testset "internal arithmetic" begin - @test Vector{Groups.FreeGroupElem}([s,t]) == [Groups.GroupWord(s), Groups.GroupWord(t)] @test (s*s).symbols == (s^2).symbols @test hash([t^1,s^1]) == hash([t^2*inv(t),s*inv(s)*s]) t_symb = Groups.FreeSymbol(:t) tt = deepcopy(t) - @test string(Groups.r_multiply!(tt,[inv(t_symb)]; reduced=true)) == - "(id)" + @test string(Groups.rmul!(tt, tt, inv(t_symb))) == "(id)" tt = deepcopy(t) - @test string(Groups.r_multiply!(tt,[inv(t_symb)]; reduced=false)) == - "t*t^-1" + @test string(append!(tt, [inv(t_symb)])) == "t*t^-1" tt = deepcopy(t) - @test string(Groups.l_multiply!(tt,[inv(t_symb)]; reduced=true)) == - "(id)" + @test string(Groups.lmul!(tt, tt, inv(t_symb))) == "(id)" tt = deepcopy(t) - @test string(Groups.l_multiply!(tt,[inv(t_symb)]; reduced=false)) == - "t^-1*t" + @test string(prepend!(tt, [inv(t_symb)])) == "t^-1*t" end @testset "reductions" begin @@ -79,7 +74,7 @@ end @test length((one(G)*one(G)).symbols) == 0 @test one(G) == one(G)*one(G) w = deepcopy(s) - push!(w.symbols, (s^-1).symbols[1]) + push!(Groups.syllables(w), (s^-1).symbols[1]) @test Groups.reduce!(w) == one(parent(w)) o = (t*s)^3 @test o == t*s*t*s*t*s @@ -116,23 +111,23 @@ end @test Groups.issubsymbol(inv(b), Groups.change_pow(b,-2)) == true c = s*t*s^-1*t^-1 - @test findfirst(c, s^-1*t^-1) == 3 - @test findnext(c*s^-1, s^-1*t^-1,3) == 3 - @test findnext(c*s^-1*t^-1, s^-1*t^-1,4) == 5 - @test findfirst(c*t, c) == 0 + @test findfirst(s^-1*t^-1, c) == 3 + @test findnext(s^-1*t^-1, c*s^-1,3) == 3 + @test findnext(s^-1*t^-1, c*s^-1*t^-1,4) == 5 + @test findfirst(c, c*t) === nothing w = s*t*s^-1 subst = Dict{FreeGroupElem, FreeGroupElem}(w => s^1, s*t^-1 => t^4) - @test Groups.replace(c, 1, s*t, one(G)) == s^-1*t^-1 - @test Groups.replace(c, 1, w, subst[w]) == s*t^-1 - @test Groups.replace(s*c*t^-1, 1, w, subst[w]) == s^2*t^-2 - @test Groups.replace(t*c*t, 2, w, subst[w]) == t*s - @test Groups.replace_all(s*c*s*c*s, subst) == s*t^4*s*t^4*s + @test Groups.replace(c, s*t=>one(G)) == s^-1*t^-1 + @test Groups.replace(c, w=>subst[w]) == s*t^-1 + @test Groups.replace(s*c*t^-1, w=>subst[w]) == s^2*t^-2 + @test Groups.replace(t*c*t, w=>subst[w]) == t*s + @test Groups.replace(s*c*s*c*s, subst) == s*t^4*s*t^4*s G = FreeGroup(["x", "y"]) x,y = gens(G) - @test Groups.replace(x*y^9, 2, y^2, y) == x*y^8 - @test Groups.replace(x^3, 1, x^2, y) == x*y - @test Groups.replace(y*x^3*y, 2, x^2, y) == y*x*y^2 + @test Groups.replace(x*y^9, y^2=>y) == x*y^5 + @test Groups.replace(x^3, x^2=>y) == x*y + @test Groups.replace(y*x^3*y, x^2=>y) == y*x*y^2 end end