280 lines
9.7 KiB
Julia
280 lines
9.7 KiB
Julia
using Groups
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using Base.Test
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# write your own tests here
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@testset "Groups" begin
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@testset "FPSymbols" begin
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s = FPSymbol("s")
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t = FPSymbol("t")
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@testset "defines" begin
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@test isa(FPSymbol(string(Char(rand(50:2000)))), GSymbol)
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@test FPSymbol("abc").pow == 1
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@test isa(s, FPSymbol)
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@test isa(t, FPSymbol)
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end
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@testset "eltary functions" begin
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@test length(s) == 1
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@test Groups.change_pow(s, 0) == Groups.change_pow(t, 0)
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@test length(Groups.change_pow(s, 0)) == 0
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@test inv(s).pow == -1
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@test FPSymbol("s", 3) == Groups.change_pow(s, 3)
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@test FPSymbol("s", 3) != FPSymbol("t", 3)
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@test Groups.change_pow(inv(s), -3) == inv(Groups.change_pow(s, 3))
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end
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@testset "powers" begin
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s⁴ = Groups.change_pow(s,4)
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@test s⁴.pow == 4
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@test Groups.change_pow(s, 4) == FPSymbol("s", 4)
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end
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end
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@testset "FPGroupElems" begin
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s = FPSymbol("s")
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t = FPSymbol("t", -2)
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@testset "defines" begin
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@test isa(Groups.GWord(s), Groups.GWord)
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@test isa(Groups.GWord(s), FPGroupElem)
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@test isa(FPGroupElem(s), Groups.GWord)
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@test isa(convert(FPGroupElem, s), GWord)
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@test isa(convert(FPGroupElem, s), FPGroupElem)
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@test isa(Vector{FPGroupElem}([s,t]), Vector{FPGroupElem})
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@test length(FPGroupElem(s)) == 1
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@test length(FPGroupElem(t)) == 2
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end
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@testset "eltary functions" begin
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@test_skip (s*s).symbols == (s^2).symbols
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@test_skip Vector{GWord{FPSymbol}}([s,t]) == Vector{FPGroupElem}([s,t])
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@test_skip Vector{GWord}([s,t]) == [GWord(s), GWord(t)]
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@test_skip hash([t^1,s^1]) == hash([t^2*inv(t),s*inv(s)*s])
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end
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end
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@testset "FPGroup" begin
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@test isa(FPGroup(["s", "t"]), Nemo.Group)
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G = FPGroup(["s", "t"])
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@testset "elements constructors" begin
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@test isa(G(), FPGroupElem)
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@test eltype(G.gens) == FPSymbol
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@test length(G.gens) == 2
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@test eltype(G.rels) == FPGroupElem
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@test length(G.rels) == 0
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@test eltype(generators(G)) == FPGroupElem
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@test length(generators(G)) == 2
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end
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s, t = generators(G)
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@testset "internal arithmetic" begin
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t_symb = FPSymbol("t")
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tt = deepcopy(t)
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@test string(Groups.r_multiply!(tt,[inv(t_symb)]; reduced=true)) ==
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"(id)"
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tt = deepcopy(t)
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@test string(Groups.r_multiply!(tt,[inv(t_symb)]; reduced=false)) ==
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"t*t^-1"
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tt = deepcopy(t)
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@test string(Groups.l_multiply!(tt,[inv(t_symb)]; reduced=true)) ==
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"(id)"
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tt = deepcopy(t)
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@test string(Groups.l_multiply!(tt,[inv(t_symb)]; reduced=false)) ==
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"t^-1*t"
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end
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@testset "reductions" begin
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@test length(G().symbols) == 1
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@test length((G()*G()).symbols) == 0
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@test G() == G()*G()
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w = deepcopy(s)
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push!(w.symbols, (s^-1).symbols[1])
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@test Groups.reduce!(w) == parent(w)()
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o = (t*s)^3
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@test o == t*s*t*s*t*s
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p = (t*s)^-3
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@test p == s^-1*t^-1*s^-1*t^-1*s^-1*t^-1
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@test o*p == parent(o*p)()
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w = FPGroupElem([o.symbols..., p.symbols...])
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w.parent = G
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@test Groups.reduce!(w).symbols ==Vector{FPSymbol}([])
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end
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@testset "binary/inv operations" begin
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@test parent(s) == G
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@test parent(s) === parent(deepcopy(s))
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@test isa(s*t, FPGroupElem)
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@test parent(s*t) == parent(s^2)
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@test s*s == s^2
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@test inv(s*s) == inv(s^2)
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@test inv(s)^2 == inv(s^2)
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@test inv(s)*inv(s) == inv(s^2)
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@test inv(s*t) == inv(t)*inv(s)
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w = s*t*s^-1
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@test inv(w) == s*t^-1*s^-1
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@test (t*s*t^-1)^10 == t*s^10*t^-1
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@test (t*s*t^-1)^-10 == t*s^-10*t^-1
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end
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@testset "replacements" begin
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a = FPSymbol("a")
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b = FPSymbol("b")
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@test Groups.is_subsymbol(a, Groups.change_pow(a,2)) == true
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@test Groups.is_subsymbol(a, Groups.change_pow(a,-2)) == false
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@test Groups.is_subsymbol(b, Groups.change_pow(a,-2)) == false
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@test Groups.is_subsymbol(inv(b), Groups.change_pow(b,-2)) == true
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c = s*t*s^-1*t^-1
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@test findfirst(c, s^-1*t^-1) == 3
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@test findnext(c*s^-1, s^-1*t^-1,3) == 3
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@test findnext(c*s^-1*t^-1, s^-1*t^-1,4) == 5
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@test findfirst(c*t, c) == 0
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w = s*t*s^-1
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subst = Dict{FPGroupElem, FPGroupElem}(w => s^1, s*t^-1 => t^4)
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@test Groups.replace(c, 1, s*t, G()) == s^-1*t^-1
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@test Groups.replace(c, 1, w, subst[w]) == s*t^-1
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@test Groups.replace(s*c*t^-1, 1, w, subst[w]) == s^2*t^-2
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@test Groups.replace(t*c*t, 2, w, subst[w]) == t*s
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@test Groups.replace_all!(s*c*s*c*s, subst) == s*t^4*s*t^4*s
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end
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end
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@testset "Automorphisms" begin
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@testset "AutSymbol" begin
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@test_throws MethodError AutSymbol("a")
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@test_throws MethodError AutSymbol("a", 1)
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f = AutSymbol("a", 1, :(a()), v -> v)
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@test isa(f, GSymbol)
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@test isa(f, AutSymbol)
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@test isa(symmetric_AutSymbol([1,2,3,4]), AutSymbol)
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@test isa(rmul_AutSymbol(1,2), AutSymbol)
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@test isa(lmul_AutSymbol(3,4), AutSymbol)
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@test isa(flip_AutSymbol(3), AutSymbol)
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end
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@testset "flip_AutSymbol correctness" begin
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a,b,c,d = [FPGroupElem(FPSymbol(i)) for i in ["a", "b", "c", "d"]]
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domain = [a,b,c,d]
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@test flip_AutSymbol(1)(domain) == [a^-1, b,c,d]
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@test flip_AutSymbol(2)(domain) == [a, b^-1,c,d]
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@test flip_AutSymbol(3)(domain) == [a, b,c^-1,d]
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@test flip_AutSymbol(4)(domain) == [a, b,c,d^-1]
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@test inv(flip_AutSymbol(1))(domain) == [a^-1, b,c,d]
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@test inv(flip_AutSymbol(2))(domain) == [a, b^-1,c,d]
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@test inv(flip_AutSymbol(3))(domain) == [a, b,c^-1,d]
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@test inv(flip_AutSymbol(4))(domain) == [a, b,c,d^-1]
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end
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@testset "symmetric_AutSymbol correctness" begin
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a,b,c,d = [FPGroupElem(FPSymbol(i)) for i in ["a", "b", "c", "d"]]
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domain = [a,b,c,d]
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σ = symmetric_AutSymbol([1,2,3,4])
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@test σ(domain) == domain
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@test inv(σ)(domain) == domain
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σ = symmetric_AutSymbol([2,3,4,1])
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@test σ(domain) == [b, c, d, a]
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@test inv(σ)(domain) == [d, a, b, c]
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σ = symmetric_AutSymbol([2,1,4,3])
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@test σ(domain) == [b, a, d, c]
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@test inv(σ)(domain) == [b, a, d, c]
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σ = symmetric_AutSymbol([2,3,1,4])
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@test σ(domain) == [b,c,a,d]
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@test inv(σ)(domain) == [c,a,b,d]
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end
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@testset "mul_AutSymbol correctness" begin
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a,b,c,d = [FPGroupElem(FPSymbol(i)) for i in ["a", "b", "c", "d"]]
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domain = [a,b,c,d]
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i,j = 1,2
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r = rmul_AutSymbol(i,j)
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l = lmul_AutSymbol(i,j)
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@test r(domain) == [a*b,b,c,d]
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@test inv(r)(domain) == [a*b^-1,b,c,d]
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@test l(domain) == [b*a,b,c,d]
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@test inv(l)(domain) == [b^-1*a,b,c,d]
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i,j = 3,1
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r = rmul_AutSymbol(i,j)
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l = lmul_AutSymbol(i,j)
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@test r(domain) == [a,b,c*a,d]
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@test inv(r)(domain) == [a,b,c*a^-1,d]
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@test l(domain) == [a,b,a*c,d]
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@test inv(l)(domain) == [a,b,a^-1*c,d]
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i,j = 4,3
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r = rmul_AutSymbol(i,j)
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l = lmul_AutSymbol(i,j)
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@test r(domain) == [a,b,c,d*c]
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@test inv(r)(domain) == [a,b,c,d*c^-1]
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@test l(domain) == [a,b,c,c*d]
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@test inv(l)(domain) == [a,b,c,c^-1*d]
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i,j = 2,4
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r = rmul_AutSymbol(i,j)
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l = lmul_AutSymbol(i,j)
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@test r(domain) == [a,b*d,c,d]
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@test inv(r)(domain) == [a,b*d^-1,c,d]
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@test l(domain) == [a,d*b,c,d]
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@test inv(l)(domain) == [a,d^-1*b,c,d]
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end
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@testset "AutWords" begin
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f = AutSymbol("a", 1, :(a()), v -> v)
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@test isa(GWord(f), GWord)
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@test isa(GWord(f), AutWord)
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@test isa(AutWord(f), AutWord)
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@test isa(f*f, AutWord)
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@test isa(f^2, AutWord)
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@test isa(f^-1, AutWord)
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end
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@testset "eltary functions" begin
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f = symmetric_AutSymbol([2,1,4,3])
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@test isa(inv(f), AutSymbol)
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@test isa(f^-1, AutWord)
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@test f^-1 == GWord(inv(f))
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@test inv(f) == f
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end
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@testset "reductions/arithmetic" begin
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f = symmetric_AutSymbol([2,1,4,3])
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f² = Groups.r_multiply(AutWord(f), [f], reduced=false)
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@test Groups.simplify_perms!(f²) == false
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@test f² == one(typeof(f*f))
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a = rmul_AutSymbol(1,2)*flip_AutSymbol(2)
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b = flip_AutSymbol(2)*inv(rmul_AutSymbol(1,2))
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@test a*b == b*a
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@test a^3 * b^3 == one(a)
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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) == 53
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end
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end
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end
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