124 lines
4.0 KiB
Julia
124 lines
4.0 KiB
Julia
using Groups
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using Base.Test
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# write your own tests here
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s = FGSymbol("s")
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t = FGSymbol("t")
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@testset "FGSymbols" begin
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@testset "defines" begin
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@test isa(FGSymbol(string(Char(rand(50:2000)))), Groups.GSymbol)
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@test FGSymbol("abc").pow == 1
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@test isa(s, FGSymbol)
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@test isa(t, FGSymbol)
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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 one(s) == s^0
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@test one(s) == one(FGSymbol)
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@test Groups.change_pow(s,0) == one(s)
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@test length(one(s)) == 0
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@test inv(s).pow == -1
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@test FGSymbol("s", 3) == Groups.change_pow(s,3)
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@test s^2 ≠ t^2
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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 (s^4).symbols[1] == Groups.change_pow(s,4)
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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*s) == inv(s)*inv(s)
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end
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end
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@testset "GWords" begin
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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), FGWord)
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@test isa(FGWord(s), Groups.GWord)
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@test isa(s*s, FGWord)
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@test s*s == s^2
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@test t*s ≠ s*t
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end
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@testset "eltary functions" begin
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@test length(FGWord(s)) == 1
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@test length(s*s) == 2
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@test length(s*s^-1) == 0
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@test length(s*t^-1) == 2
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@test isa(one(FGWord), FGWord)
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@test one(FGWord).symbols == Vector{FGSymbol}([one(FGSymbol)])
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@test isa(one(Groups.GWord{FGSymbol}), Groups.GWord{FGSymbol})
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w = s*t*s^-1
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@test isa(one(w), FGWord)
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@test inv(s*t) == t^-1*s^-1
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@test inv(w) == s*t^-1*s^-1
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end
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@testset "reductions" begin
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@test one(FGWord) == one(s)*one(s)
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w = GWord{FGSymbol}([s])
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push!(w.symbols, (s^-1).symbols[1])
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@test Groups.freegroup_reduce!(w) == one(FGWord)
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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 == one(FGWord)
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w = FGWord([o.symbols..., p.symbols...])
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@test Groups.freegroup_reduce!(w).symbols ==Vector{FGSymbol}([])
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end
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@testset "arithmetic" begin
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@test Groups.r_multiply!(FGWord(t),[s,t]; reduced=true) == t*s*t
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@test Groups.r_multiply!(FGWord(t),[s,t]; reduced=false) == t*s*t
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@test Groups.l_multiply!(FGWord(t),[s,t]; reduced=true) == t*s*t
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@test Groups.l_multiply!(FGWord(t),[s,t]; reduced=false) == t*s*t
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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 "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(0)))
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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 "AutWords" begin
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f = AutSymbol("a", 1, :(a(0)))
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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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end
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