149 lines
4.8 KiB
Julia
149 lines
4.8 KiB
Julia
@testset "Groups.FreeSymbols" begin
|
|
s = Groups.FreeSymbol(:s)
|
|
t = Groups.FreeSymbol(:t)
|
|
|
|
@testset "constructors" begin
|
|
@test isa(Groups.FreeSymbol(:aaaaaaaaaaaaaaaa), Groups.GSymbol)
|
|
@test Groups.FreeSymbol(:abc).pow == 1
|
|
@test isa(s, Groups.FreeSymbol)
|
|
@test isa(t, Groups.FreeSymbol)
|
|
end
|
|
@testset "eltary functions" begin
|
|
@test length(s) == 1
|
|
@test Groups.change_pow(s, 0) == Groups.change_pow(t, 0)
|
|
@test length(Groups.change_pow(s, 0)) == 0
|
|
@test inv(s).pow == -1
|
|
@test Groups.FreeSymbol(:s, 3) == Groups.change_pow(s, 3)
|
|
@test Groups.FreeSymbol(:s, 3) != Groups.FreeSymbol(:t, 3)
|
|
@test Groups.change_pow(inv(s), -3) == inv(Groups.change_pow(s, 3))
|
|
end
|
|
@testset "powers" begin
|
|
s⁴ = Groups.change_pow(s,4)
|
|
@test s⁴.pow == 4
|
|
@test Groups.change_pow(s, 4) == Groups.FreeSymbol(:s, 4)
|
|
end
|
|
end
|
|
|
|
@testset "FreeGroupSymbols manipulation" begin
|
|
s = Groups.FreeSymbol("s")
|
|
t = Groups.FreeSymbol(:t, -2)
|
|
|
|
@test isa(Groups.GroupWord(s), Groups.GWord{Groups.FreeSymbol})
|
|
@test isa(Groups.GroupWord(s), FreeGroupElem)
|
|
@test isa(FreeGroupElem(s), Groups.GWord)
|
|
@test isa(convert(FreeGroupElem, s), Groups.GWord)
|
|
@test isa(convert(FreeGroupElem, s), FreeGroupElem)
|
|
@test isa(Vector{FreeGroupElem}([s,t]), Vector{FreeGroupElem})
|
|
@test length(FreeGroupElem(s)) == 1
|
|
@test length(FreeGroupElem(t)) == 2
|
|
|
|
end
|
|
|
|
@testset "FreeGroup" begin
|
|
@test isa(FreeGroup(["s", "t"]), AbstractAlgebra.Group)
|
|
G = FreeGroup(["s", "t"])
|
|
|
|
@testset "elements constructors" begin
|
|
@test isa(one(G), FreeGroupElem)
|
|
@test eltype(G.gens) == Groups.FreeSymbol
|
|
@test length(G.gens) == 2
|
|
@test eltype(gens(G)) == FreeGroupElem
|
|
@test length(gens(G)) == 2
|
|
end
|
|
|
|
s, t = gens(G)
|
|
|
|
@testset "internal arithmetic" begin
|
|
|
|
@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.rmul!(tt, tt, inv(tt))) == "(id)"
|
|
tt = deepcopy(t)
|
|
@test string(Groups.lmul!(tt, tt, inv(tt))) == "(id)"
|
|
|
|
tt = deepcopy(t)
|
|
push!(tt, inv(t_symb))
|
|
@test string(tt) == "t*t^-1"
|
|
tt = deepcopy(t)
|
|
pushfirst!(tt, inv(t_symb))
|
|
@test string(tt) == "t^-1*t"
|
|
|
|
tt = deepcopy(t)
|
|
append!(tt, inv(t))
|
|
@test string(tt) == "t*t^-1"
|
|
|
|
tt = deepcopy(t)
|
|
prepend!(tt, inv(t))
|
|
@test string(tt) == "t^-1*t"
|
|
|
|
tt = deepcopy(t)
|
|
append!(tt, s, inv(t))
|
|
@test string(tt) == "t*s*t^-1"
|
|
end
|
|
|
|
@testset "reductions" begin
|
|
@test length(one(G).symbols) == 0
|
|
@test length((one(G)*one(G)).symbols) == 0
|
|
@test one(G) == one(G)*one(G)
|
|
w = deepcopy(s)
|
|
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
|
|
p = (t*s)^-3
|
|
@test p == s^-1*t^-1*s^-1*t^-1*s^-1*t^-1
|
|
@test o*p == one(parent(o*p))
|
|
w = FreeGroupElem([o.symbols..., p.symbols...])
|
|
w.parent = G
|
|
@test Groups.reduce!(w).symbols ==Vector{Groups.FreeSymbol}([])
|
|
end
|
|
|
|
@testset "Group operations" begin
|
|
@test parent(s) == G
|
|
@test parent(s) === parent(deepcopy(s))
|
|
@test isa(s*t, FreeGroupElem)
|
|
@test parent(s*t) == parent(s^2)
|
|
@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*t) == inv(t)*inv(s)
|
|
w = s*t*s^-1
|
|
@test inv(w) == s*t^-1*s^-1
|
|
@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
|
|
a = Groups.FreeSymbol(:a)
|
|
b = Groups.FreeSymbol(:b)
|
|
@test Groups.issubsymbol(a, Groups.change_pow(a,2)) == true
|
|
@test Groups.issubsymbol(a, Groups.change_pow(a,-2)) == false
|
|
@test Groups.issubsymbol(b, Groups.change_pow(a,-2)) == false
|
|
@test Groups.issubsymbol(inv(b), Groups.change_pow(b,-2)) == true
|
|
|
|
c = s*t*s^-1*t^-1
|
|
@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, 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, 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
|