kalmar/Groups.jl
1
0
Fork 0
mirror of https://github.com/kalmarek/Groups.jl.git synced 2024-09-13 08:25:39 +02:00
Code Issues Releases Wiki Activity

fix tests

Browse Source
This commit is contained in:
kalmarek 2020-03-25 05:25:02 +01:00
parent ac4ee69fc6
commit 7d95338e33
No known key found for this signature in database
GPG Key ID: 8BF1A3855328FC15
3 changed files with 87 additions and 92 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

127
test/AutGroup-tests.jl
View File

@ -8,72 +8,73 @@
f = Groups.AutSymbol(:a, 1, Groups.FlipAut(2)) f = Groups.AutSymbol(:a, 1, Groups.FlipAut(2))
@test isa(f, Groups.GSymbol) @test isa(f, Groups.GSymbol)
@test isa(f, Groups.AutSymbol) @test isa(f, Groups.AutSymbol)
@test isa(Groups.perm_autsymbol(Int8.([1,2,3,4])), Groups.AutSymbol) @test isa(Groups.AutSymbol(perm"(4)"), Groups.AutSymbol)
@test isa(Groups.rmul_autsymbol(1,2), Groups.AutSymbol) @test isa(Groups.AutSymbol([2,3,4,1]), Groups.AutSymbol)
@test isa(Groups.lmul_autsymbol(3,4), Groups.AutSymbol) @test isa(Groups.transvection_R(1,2), Groups.AutSymbol)
@test isa(Groups.flip_autsymbol(3), Groups.AutSymbol) @test isa(Groups.transvection_R(3,4), Groups.AutSymbol)
@test isa(Groups.flip(3), Groups.AutSymbol)
end end
a,b,c,d = gens(FreeGroup(4)) a,b,c,d = gens(FreeGroup(4))
D = NTuple{4,FreeGroupElem}([a,b,c,d]) D = NTuple{4,FreeGroupElem}([a,b,c,d])
@testset "flip_autsymbol correctness" begin @testset "flip correctness" begin
@test Groups.flip_autsymbol(1)(deepcopy(D)) == (a^-1, b,c,d) @test Groups.flip(1)(deepcopy(D)) == (a^-1, b,c,d)
@test Groups.flip_autsymbol(2)(deepcopy(D)) == (a, b^-1,c,d) @test Groups.flip(2)(deepcopy(D)) == (a, b^-1,c,d)
@test Groups.flip_autsymbol(3)(deepcopy(D)) == (a, b,c^-1,d) @test Groups.flip(3)(deepcopy(D)) == (a, b,c^-1,d)
@test Groups.flip_autsymbol(4)(deepcopy(D)) == (a, b,c,d^-1) @test Groups.flip(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(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(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(3))(deepcopy(D)) == (a, b,c^-1,d)
@test inv(Groups.flip_autsymbol(4))(deepcopy(D)) == (a, b,c,d^-1) @test inv(Groups.flip(4))(deepcopy(D)) == (a, b,c,d^-1)
end end
@testset "perm_autsymbol correctness" begin @testset "perm correctness" begin
σ = Groups.perm_autsymbol([1,2,3,4]) σ = Groups.AutSymbol(perm"(4)")
@test σ(deepcopy(D)) == deepcopy(D) @test σ(deepcopy(D)) == deepcopy(D)
@test inv(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 σ(deepcopy(D)) == (b, c, d, a)
@test inv(σ)(deepcopy(D)) == (d, a, b, c) @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 σ(deepcopy(D)) == (b, a, d, c)
@test inv(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 σ(deepcopy(D)) == (b, c, a, d)
@test inv(σ)(deepcopy(D)) == (c, a, b, d) @test inv(σ)(deepcopy(D)) == (c, a, b, d)
end end
@testset "rmul/lmul_autsymbol correctness" begin @testset "rmul/transvection_R correctness" begin
i,j = 1,2 i,j = 1,2
r = Groups.rmul_autsymbol(i,j) r = Groups.transvection_R(i,j)
l = Groups.lmul_autsymbol(i,j) l = Groups.transvection_L(i,j)
@test r(deepcopy(D)) == (a*b, b, c, d) @test r(deepcopy(D)) == (a*b, b, c, d)
@test inv(r)(deepcopy(D)) == (a*b^-1,b, c, d) @test inv(r)(deepcopy(D)) == (a*b^-1,b, c, d)
@test l(deepcopy(D)) == (b*a, b, c, d) @test l(deepcopy(D)) == (b*a, b, c, d)
@test inv(l)(deepcopy(D)) == (b^-1*a,b, c, d) @test inv(l)(deepcopy(D)) == (b^-1*a,b, c, d)
i,j = 3,1 i,j = 3,1
r = Groups.rmul_autsymbol(i,j) r = Groups.transvection_R(i,j)
l = Groups.lmul_autsymbol(i,j) l = Groups.transvection_L(i,j)
@test r(deepcopy(D)) == (a, b, c*a, d) @test r(deepcopy(D)) == (a, b, c*a, d)
@test inv(r)(deepcopy(D)) == (a, b, c*a^-1,d) @test inv(r)(deepcopy(D)) == (a, b, c*a^-1,d)
@test l(deepcopy(D)) == (a, b, a*c, d) @test l(deepcopy(D)) == (a, b, a*c, d)
@test inv(l)(deepcopy(D)) == (a, b, a^-1*c,d) @test inv(l)(deepcopy(D)) == (a, b, a^-1*c,d)
i,j = 4,3 i,j = 4,3
r = Groups.rmul_autsymbol(i,j) r = Groups.transvection_R(i,j)
l = Groups.lmul_autsymbol(i,j) l = Groups.transvection_L(i,j)
@test r(deepcopy(D)) == (a, b, c, d*c) @test r(deepcopy(D)) == (a, b, c, d*c)
@test inv(r)(deepcopy(D)) == (a, b, c, d*c^-1) @test inv(r)(deepcopy(D)) == (a, b, c, d*c^-1)
@test l(deepcopy(D)) == (a, b, c, c*d) @test l(deepcopy(D)) == (a, b, c, c*d)
@test inv(l)(deepcopy(D)) == (a, b, c, c^-1*d) @test inv(l)(deepcopy(D)) == (a, b, c, c^-1*d)
i,j = 2,4 i,j = 2,4
r = Groups.rmul_autsymbol(i,j) r = Groups.transvection_R(i,j)
l = Groups.lmul_autsymbol(i,j) l = Groups.transvection_L(i,j)
@test r(deepcopy(D)) == (a, b*d, c, d) @test r(deepcopy(D)) == (a, b*d, c, d)
@test inv(r)(deepcopy(D)) == (a, b*d^-1,c, d) @test inv(r)(deepcopy(D)) == (a, b*d^-1,c, d)
@test l(deepcopy(D)) == (a, d*b, c, d) @test l(deepcopy(D)) == (a, d*b, c, d)
@ -94,40 +95,40 @@
@test length(Groups.gens(A)) == 0 @test length(Groups.gens(A)) == 0
A = AutGroup(FreeGroup(2)) A = AutGroup(FreeGroup(2))
@test length(Groups.gens(A)) == 7 @test length(Groups.gens(A)) == 7
gens = Groups.gens(A) Agens = Groups.gens(A)
@test isa(A(Groups.rmul_autsymbol(1,2)), Automorphism) @test isa(A(Groups.transvection_R(1,2)), Automorphism)
@test A(Groups.rmul_autsymbol(1,2)) in gens @test A(Groups.transvection_R(1,2)) in Agens
@test isa(A(Groups.rmul_autsymbol(2,1)), Automorphism) @test isa(A(Groups.transvection_R(2,1)), Automorphism)
@test A(Groups.rmul_autsymbol(2,1)) in gens @test A(Groups.transvection_R(2,1)) in Agens
@test isa(A(Groups.lmul_autsymbol(1,2)), Automorphism) @test isa(A(Groups.transvection_R(1,2)), Automorphism)
@test A(Groups.lmul_autsymbol(1,2)) in gens @test A(Groups.transvection_R(1,2)) in Agens
@test isa(A(Groups.lmul_autsymbol(2,1)), Automorphism) @test isa(A(Groups.transvection_R(2,1)), Automorphism)
@test A(Groups.lmul_autsymbol(2,1)) in gens @test A(Groups.transvection_R(2,1)) in Agens
@test isa(A(Groups.flip_autsymbol(1)), Automorphism) @test isa(A(Groups.flip(1)), Automorphism)
@test A(Groups.flip_autsymbol(1)) in gens @test A(Groups.flip(1)) in Agens
@test isa(A(Groups.flip_autsymbol(2)), Automorphism) @test isa(A(Groups.flip(2)), Automorphism)
@test A(Groups.flip_autsymbol(2)) in gens @test A(Groups.flip(2)) in Agens
@test isa(A(Groups.perm_autsymbol([2,1])), Automorphism) @test isa(A(Groups.AutSymbol(perm"(1,2)")), Automorphism)
@test A(Groups.perm_autsymbol([2,1])) in gens @test A(Groups.AutSymbol(perm"(1,2)")) in Agens
end end
A = AutGroup(FreeGroup(4)) A = AutGroup(FreeGroup(4))
@testset "eltary functions" begin @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 (Groups.change_pow(f, -2)).pow == 1 @test (Groups.change_pow(f, -2)).pow == 1
@test (inv(f)).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 isa(inv(f), Groups.AutSymbol)
@test_throws MethodError f*f @test_throws MethodError f*f
@ -136,14 +137,15 @@
end end
@testset "reductions/arithmetic" begin @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) f² = append!(A(f), [f])
@test Groups.simplifyperms!(f²) == false @test Groups.simplifyperms!(Bool, f²) == false
@test f²^2 == one(A) @test f²^2 == one(A)
@test !isone(f²)
a = A(Groups.rmul_autsymbol(1,2))*Groups.flip_autsymbol(2) a = A(Groups.transvection_L(1,2))*Groups.flip(2)
b = Groups.flip_autsymbol(2)*A(inv(Groups.rmul_autsymbol(1,2))) b = Groups.flip(2)*A(inv(Groups.transvection_L(1,2)))
@test a*b == b*a @test a*b == b*a
@test a^3 * b^3 == one(A) @test a^3 * b^3 == one(A)
g,h = Groups.gens(A)[[1,8]] # (g, h) = (ϱ₁₂, ϱ₃₂) g,h = Groups.gens(A)[[1,8]] # (g, h) = (ϱ₁₂, ϱ₃₂)
@ -164,27 +166,22 @@
# Not so simple arithmetic: applying starting on the left: # Not so simple arithmetic: applying starting on the left:
# ϱ₁₂*ϱ₂₁⁻¹*λ₁₂*ε₂ == σ₂₁₃₄ # 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) x1, x2, x3, x4 = Groups.domain(A)
@test g(Groups.domain(A)) == (x1*x2, x2, x3, x4) @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) @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) @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)) == (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)) g_im = g(Groups.domain(A))
@test length(g_im[1]) == 5 @test length.(g_im) == (1,1,1,1)
@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)
end end
@testset "specific Aut(F4) tests" begin @testset "specific Aut(F4) tests" begin
@ -219,8 +216,8 @@
M = Matrix{Int}(I, N, N) M = Matrix{Int}(I, N, N)
M[1,2] = 1 M[1,2] = 1
ϱ₁₂ = G(Groups.rmul_autsymbol(1,2)) ϱ₁₂ = G(Groups.transvection_R(1,2))
λ₁₂ = G(Groups.rmul_autsymbol(1,2)) λ₁₂ = G(Groups.transvection_R(1,2))
@test Groups.linear_repr(ϱ₁₂) == M @test Groups.linear_repr(ϱ₁₂) == M
@test Groups.linear_repr(λ₁₂) == M @test Groups.linear_repr(λ₁₂) == M
@ -235,14 +232,14 @@
M = Matrix{Int}(I, N, N) M = Matrix{Int}(I, N, N)
M[2,2] = -1 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) == M
@test Groups.linear_repr(ε₂^2) == Matrix{Int}(I, N, N) @test Groups.linear_repr(ε₂^2) == Matrix{Int}(I, N, N)
M = [0 1 0; 0 0 1; 1 0 0] 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) == M
@test Groups.linear_repr(σ^3) == Matrix{Int}(I, 3, 3) @test Groups.linear_repr(σ^3) == Matrix{Int}(I, 3, 3)
@test Groups.linear_repr(σ)^3 == Matrix{Int}(I, 3, 3) @test Groups.linear_repr(σ)^3 == Matrix{Int}(I, 3, 3)

13
test/FPGroup-tests.jl
View File

@ -1,15 +1,18 @@
@testset "FPGroups definitions" begin @testset "FPGroups definitions" begin
F = FreeGroup(["a", "b", "c"]) 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] R = [a^2, a*b*a, c*b*a]
@test F/R isa FPGroup @test F/R isa FPGroup
@test F isa FreeGroup @test F isa FreeGroup
G = F/R G = F/R
A,B,C = gens(G) A,B,C = Groups.gens(G)
@test A^2 == one(G) @test Groups.reduce!(A^2) == one(G)
@test A*B*A*A == A @test Groups.reduce!(A*B*A*A) == A
@test A*A*B*A == B*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 @test G/[B^2, C*B*C] isa FPGroup
end end

39
test/FreeGroup-tests.jl
View File

@ -55,23 +55,18 @@ end
@testset "internal arithmetic" begin @testset "internal arithmetic" begin
@test Vector{Groups.FreeGroupElem}([s,t]) == [Groups.GroupWord(s), Groups.GroupWord(t)]
@test (s*s).symbols == (s^2).symbols @test (s*s).symbols == (s^2).symbols
@test hash([t^1,s^1]) == hash([t^2*inv(t),s*inv(s)*s]) @test hash([t^1,s^1]) == hash([t^2*inv(t),s*inv(s)*s])
t_symb = Groups.FreeSymbol(:t) t_symb = Groups.FreeSymbol(:t)
tt = deepcopy(t) tt = deepcopy(t)
@test string(Groups.r_multiply!(tt,[inv(t_symb)]; reduced=true)) == @test string(Groups.rmul!(tt, tt, inv(t_symb))) == "(id)"
"(id)"
tt = deepcopy(t) tt = deepcopy(t)
@test string(Groups.r_multiply!(tt,[inv(t_symb)]; reduced=false)) == @test string(append!(tt, [inv(t_symb)])) == "t*t^-1"
"t*t^-1"
tt = deepcopy(t) tt = deepcopy(t)
@test string(Groups.l_multiply!(tt,[inv(t_symb)]; reduced=true)) == @test string(Groups.lmul!(tt, tt, inv(t_symb))) == "(id)"
"(id)"
tt = deepcopy(t) tt = deepcopy(t)
@test string(Groups.l_multiply!(tt,[inv(t_symb)]; reduced=false)) == @test string(prepend!(tt, [inv(t_symb)])) == "t^-1*t"
"t^-1*t"
end end
@testset "reductions" begin @testset "reductions" begin
@ -79,7 +74,7 @@ end
@test length((one(G)*one(G)).symbols) == 0 @test length((one(G)*one(G)).symbols) == 0
@test one(G) == one(G)*one(G) @test one(G) == one(G)*one(G)
w = deepcopy(s) 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)) @test Groups.reduce!(w) == one(parent(w))
o = (t*s)^3 o = (t*s)^3
@test o == t*s*t*s*t*s @test o == t*s*t*s*t*s
@ -116,23 +111,23 @@ end
@test Groups.issubsymbol(inv(b), Groups.change_pow(b,-2)) == true @test Groups.issubsymbol(inv(b), Groups.change_pow(b,-2)) == true
c = s*t*s^-1*t^-1 c = s*t*s^-1*t^-1
@test findfirst(c, s^-1*t^-1) == 3 @test findfirst(s^-1*t^-1, c) == 3
@test findnext(c*s^-1, s^-1*t^-1,3) == 3 @test findnext(s^-1*t^-1, c*s^-1,3) == 3
@test findnext(c*s^-1*t^-1, s^-1*t^-1,4) == 5 @test findnext(s^-1*t^-1, c*s^-1*t^-1,4) == 5
@test findfirst(c*t, c) == 0 @test findfirst(c, c*t) === nothing
w = s*t*s^-1 w = s*t*s^-1
subst = Dict{FreeGroupElem, FreeGroupElem}(w => s^1, s*t^-1 => t^4) 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, s*t=>one(G)) == s^-1*t^-1
@test Groups.replace(c, 1, w, subst[w]) == s*t^-1 @test Groups.replace(c, w=>subst[w]) == s*t^-1
@test Groups.replace(s*c*t^-1, 1, w, subst[w]) == s^2*t^-2 @test Groups.replace(s*c*t^-1, w=>subst[w]) == s^2*t^-2
@test Groups.replace(t*c*t, 2, w, subst[w]) == t*s @test Groups.replace(t*c*t, 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(s*c*s*c*s, subst) == s*t^4*s*t^4*s
G = FreeGroup(["x", "y"]) G = FreeGroup(["x", "y"])
x,y = gens(G) x,y = gens(G)
@test Groups.replace(x*y^9, 2, y^2, y) == x*y^8 @test Groups.replace(x*y^9, y^2=>y) == x*y^5
@test Groups.replace(x^3, 1, x^2, y) == x*y @test Groups.replace(x^3, x^2=>y) == x*y
@test Groups.replace(y*x^3*y, 2, x^2, y) == y*x*y^2 @test Groups.replace(y*x^3*y, x^2=>y) == y*x*y^2
end end
end end