246 lines
8.5 KiB
Julia
246 lines
8.5 KiB
Julia
using Groups
|
||
using Base.Test
|
||
|
||
# write your own tests here
|
||
s = FGSymbol("s")
|
||
t = FGSymbol("t")
|
||
|
||
@testset "FGSymbols" begin
|
||
@testset "defines" begin
|
||
@test isa(FGSymbol(string(Char(rand(50:2000)))), Groups.GSymbol)
|
||
@test FGSymbol("abc").pow == 1
|
||
@test isa(s, FGSymbol)
|
||
@test isa(t, FGSymbol)
|
||
end
|
||
@testset "eltary functions" begin
|
||
@test length(s) == 1
|
||
@test one(s) == s^0
|
||
@test one(s) == one(FGSymbol)
|
||
@test Groups.change_pow(s,0) == one(s)
|
||
@test length(one(s)) == 0
|
||
@test inv(s).pow == -1
|
||
@test FGSymbol("s", 3) == Groups.change_pow(s,3)
|
||
@test s^2 ≠ t^2
|
||
|
||
end
|
||
@testset "powers" begin
|
||
s⁴ = Groups.change_pow(s,4)
|
||
@test s⁴.pow == 4
|
||
@test (s^4).symbols[1] == Groups.change_pow(s,4)
|
||
@test s*s == s^2
|
||
@test inv(s*s) == inv(s^2)
|
||
@test inv(s)^2 == inv(s^2)
|
||
@test inv(s)*inv(s) == inv(s^2)
|
||
@test inv(s*s) == inv(s)*inv(s)
|
||
end
|
||
end
|
||
|
||
@testset "FGWords" begin
|
||
@testset "defines" begin
|
||
@test isa(Groups.GWord(s), Groups.GWord)
|
||
@test isa(Groups.GWord(s), FGWord)
|
||
@test isa(FGWord(s), Groups.GWord)
|
||
@test isa(convert(FGWord, s), GWord)
|
||
@test isa(convert(FGWord, s), FGWord)
|
||
@test isa(Vector{FGWord}([s,t]), Vector{FGWord})
|
||
@test Vector{GWord{FGSymbol}}([s,t]) == Vector{FGWord}([s,t])
|
||
@test isa(s*s, FGWord)
|
||
@test s*s == s^2
|
||
@test t*s ≠ s*t
|
||
@test Vector{GWord}([s,t]) == [s^2*s^-1, t]
|
||
@test hash([t^1,s^1]) == hash([t^2*inv(t),s*inv(s)*s])
|
||
end
|
||
@testset "eltary functions" begin
|
||
@test length(FGWord(s)) == 1
|
||
@test length(s*s) == 2
|
||
@test length(s*s^-1) == 0
|
||
@test length(s*t^-1) == 2
|
||
@test isa(one(FGWord), FGWord)
|
||
@test one(FGWord).symbols == Vector{FGSymbol}([one(FGSymbol)])
|
||
@test isa(one(Groups.GWord{FGSymbol}), Groups.GWord{FGSymbol})
|
||
w = s*t*s^-1
|
||
@test isa(one(w), FGWord)
|
||
@test inv(s*t) == t^-1*s^-1
|
||
@test inv(w) == s*t^-1*s^-1
|
||
|
||
end
|
||
|
||
@testset "reductions" begin
|
||
@test one(FGWord) == one(s)*one(s)
|
||
w = GWord{FGSymbol}([s])
|
||
push!(w.symbols, (s^-1).symbols[1])
|
||
@test Groups.reduce!(w) == one(FGWord)
|
||
o = (t*s)^3
|
||
@test o == t*s*t*s*t*s
|
||
p = (t*s)^-3
|
||
@test p == s^-1*t^-1*s^-1*t^-1*s^-1*t^-1
|
||
@test o*p == one(FGWord)
|
||
w = FGWord([o.symbols..., p.symbols...])
|
||
@test Groups.reduce!(w).symbols ==Vector{FGSymbol}([])
|
||
end
|
||
@testset "arithmetic" begin
|
||
@test Groups.r_multiply!(FGWord(t),[s,t]; reduced=true) == t*s*t
|
||
@test Groups.r_multiply!(FGWord(t),[s,t]; reduced=false) == t*s*t
|
||
|
||
@test Groups.l_multiply!(FGWord(t),[s,t]; reduced=true) == t*s*t
|
||
@test Groups.l_multiply!(FGWord(t),[s,t]; reduced=false) == t*s*t
|
||
@test (t*s*t^-1)^10 == t*s^10*t^-1
|
||
@test (t*s*t^-1)^-10 == t*s^-10*t^-1
|
||
end
|
||
|
||
@testset "replacements" begin
|
||
@test Groups.is_subsymbol(s, Groups.change_pow(s,2)) == true
|
||
@test Groups.is_subsymbol(s, Groups.change_pow(s,-2)) == false
|
||
@test Groups.is_subsymbol(t, Groups.change_pow(s,-2)) == false
|
||
@test Groups.is_subsymbol(inv(t), Groups.change_pow(t,-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
|
||
w = s*t*s^-1
|
||
subst = Dict{FGWord, FGWord}(w => s^1, s*t^-1 => t^4)
|
||
@test Groups.replace(c, 1, s*t, one(FGWord)) == 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
|
||
end
|
||
end
|
||
|
||
@testset "Automorphisms" begin
|
||
@testset "AutSymbol" begin
|
||
@test_throws MethodError AutSymbol("a")
|
||
@test_throws MethodError AutSymbol("a", 1)
|
||
f = AutSymbol("a", 1, :(a()), v -> v)
|
||
@test isa(f, GSymbol)
|
||
@test isa(f, AutSymbol)
|
||
@test isa(symmetric_AutSymbol([1,2,3,4]), AutSymbol)
|
||
@test isa(rmul_AutSymbol(1,2), AutSymbol)
|
||
@test isa(lmul_AutSymbol(3,4), AutSymbol)
|
||
@test isa(flip_AutSymbol(3), AutSymbol)
|
||
end
|
||
|
||
@testset "flip_AutSymbol correctness" begin
|
||
a,b,c,d = [FGWord(FGSymbol(i)) for i in ["a", "b", "c", "d"]]
|
||
domain = [a,b,c,d]
|
||
@test flip_AutSymbol(1)(domain) == [a^-1, b,c,d]
|
||
@test flip_AutSymbol(2)(domain) == [a, b^-1,c,d]
|
||
@test flip_AutSymbol(3)(domain) == [a, b,c^-1,d]
|
||
@test flip_AutSymbol(4)(domain) == [a, b,c,d^-1]
|
||
@test inv(flip_AutSymbol(1))(domain) == [a^-1, b,c,d]
|
||
@test inv(flip_AutSymbol(2))(domain) == [a, b^-1,c,d]
|
||
@test inv(flip_AutSymbol(3))(domain) == [a, b,c^-1,d]
|
||
@test inv(flip_AutSymbol(4))(domain) == [a, b,c,d^-1]
|
||
end
|
||
|
||
@testset "symmetric_AutSymbol correctness" begin
|
||
a,b,c,d = [FGWord(FGSymbol(i)) for i in ["a", "b", "c", "d"]]
|
||
domain = [a,b,c,d]
|
||
σ = symmetric_AutSymbol([1,2,3,4])
|
||
@test σ(domain) == domain
|
||
@test inv(σ)(domain) == domain
|
||
|
||
σ = symmetric_AutSymbol([2,3,4,1])
|
||
@test σ(domain) == [b, c, d, a]
|
||
@test inv(σ)(domain) == [d, a, b, c]
|
||
|
||
σ = symmetric_AutSymbol([2,1,4,3])
|
||
@test σ(domain) == [b, a, d, c]
|
||
@test inv(σ)(domain) == [b, a, d, c]
|
||
|
||
σ = symmetric_AutSymbol([2,3,1,4])
|
||
@test σ(domain) == [b,c,a,d]
|
||
@test inv(σ)(domain) == [c,a,b,d]
|
||
end
|
||
|
||
@testset "mul_AutSymbol correctness" begin
|
||
a,b,c,d = [FGWord(FGSymbol(i)) for i in ["a", "b", "c", "d"]]
|
||
domain = [a,b,c,d]
|
||
i,j = 1,2
|
||
r = rmul_AutSymbol(i,j)
|
||
l = lmul_AutSymbol(i,j)
|
||
@test r(domain) == [a*b,b,c,d]
|
||
@test inv(r)(domain) == [a*b^-1,b,c,d]
|
||
@test l(domain) == [b*a,b,c,d]
|
||
@test inv(l)(domain) == [b^-1*a,b,c,d]
|
||
|
||
i,j = 3,1
|
||
r = rmul_AutSymbol(i,j)
|
||
l = lmul_AutSymbol(i,j)
|
||
@test r(domain) == [a,b,c*a,d]
|
||
@test inv(r)(domain) == [a,b,c*a^-1,d]
|
||
@test l(domain) == [a,b,a*c,d]
|
||
@test inv(l)(domain) == [a,b,a^-1*c,d]
|
||
|
||
|
||
i,j = 4,3
|
||
r = rmul_AutSymbol(i,j)
|
||
l = lmul_AutSymbol(i,j)
|
||
@test r(domain) == [a,b,c,d*c]
|
||
@test inv(r)(domain) == [a,b,c,d*c^-1]
|
||
@test l(domain) == [a,b,c,c*d]
|
||
@test inv(l)(domain) == [a,b,c,c^-1*d]
|
||
|
||
|
||
i,j = 2,4
|
||
r = rmul_AutSymbol(i,j)
|
||
l = lmul_AutSymbol(i,j)
|
||
@test r(domain) == [a,b*d,c,d]
|
||
@test inv(r)(domain) == [a,b*d^-1,c,d]
|
||
@test l(domain) == [a,d*b,c,d]
|
||
@test inv(l)(domain) == [a,d^-1*b,c,d]
|
||
end
|
||
|
||
|
||
@testset "AutWords" begin
|
||
f = AutSymbol("a", 1, :(a()), v -> v)
|
||
@test isa(GWord(f), GWord)
|
||
@test isa(GWord(f), AutWord)
|
||
@test isa(AutWord(f), AutWord)
|
||
@test isa(f*f, AutWord)
|
||
@test isa(f^2, AutWord)
|
||
@test isa(f^-1, AutWord)
|
||
end
|
||
@testset "eltary functions" begin
|
||
f = symmetric_AutSymbol([2,1,4,3])
|
||
@test isa(inv(f), AutSymbol)
|
||
@test isa(f^-1, AutWord)
|
||
@test f^-1 == GWord(inv(f))
|
||
@test inv(f) == f
|
||
end
|
||
@testset "reductions/arithmetic" begin
|
||
f = symmetric_AutSymbol([2,1,4,3])
|
||
f² = Groups.r_multiply(AutWord(f), [f], reduced=false)
|
||
@test Groups.simplify_perms!(f²) == false
|
||
@test f² == one(typeof(f*f))
|
||
|
||
a = rmul_AutSymbol(1,2)*flip_AutSymbol(2)
|
||
b = flip_AutSymbol(2)*inv(rmul_AutSymbol(1,2))
|
||
@test a*b == b*a
|
||
@test a^3 * b^3 == one(a)
|
||
end
|
||
@testset "specific Aut(𝔽₄) tests" begin
|
||
N = 4
|
||
import Combinatorics.nthperm
|
||
SymmetricGroup(n) = [nthperm(collect(1:n), k) for k in 1:factorial(n)]
|
||
indexing = [[i,j] for i in 1:N for j in 1:N if i≠j]
|
||
|
||
σs = [symmetric_AutSymbol(perm) for perm in SymmetricGroup(N)[2:end]];
|
||
ϱs = [rmul_AutSymbol(i,j) for (i,j) in indexing]
|
||
λs = [lmul_AutSymbol(i,j) for (i,j) in indexing]
|
||
ɛs = [flip_AutSymbol(i) for i in 1:N];
|
||
|
||
S = vcat(ϱs, λs, σs, ɛs)
|
||
S = vcat(S, [inv(s) for s in S])
|
||
@test isa(S, Vector{AutSymbol})
|
||
@test length(S) == 102
|
||
@test length(unique(S)) == 75
|
||
S₁ = [GWord(s) for s in unique(S)]
|
||
@test isa(S₁, Vector{AutWord})
|
||
p = prod(S₁)
|
||
@test length(p) == 53
|
||
end
|
||
end
|