140 lines
4.7 KiB
Julia
140 lines
4.7 KiB
Julia
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@testset "Groups.FreeSymbols" begin
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s = Groups.FreeSymbol("s")
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t = Groups.FreeSymbol("t")
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@testset "constructors" begin
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@test isa(Groups.FreeSymbol("aaaaaaaaaaaaaaaa"), Groups.GSymbol)
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@test Groups.FreeSymbol("abc").pow == 1
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@test isa(s, Groups.FreeSymbol)
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@test isa(t, Groups.FreeSymbol)
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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 Groups.FreeSymbol("s", 3) == Groups.change_pow(s, 3)
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@test Groups.FreeSymbol("s", 3) != Groups.FreeSymbol("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) == Groups.FreeSymbol("s", 4)
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end
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end
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@testset "FreeGroupSymbols manipulation" begin
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s = Groups.FreeSymbol("s")
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t = Groups.FreeSymbol("t", -2)
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@test isa(Groups.GroupWord(s), Groups.GWord{Groups.FreeSymbol})
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@test isa(Groups.GroupWord(s), FreeGroupElem)
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@test isa(FreeGroupElem(s), Groups.GWord)
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@test isa(convert(FreeGroupElem, s), Groups.GWord)
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@test isa(convert(FreeGroupElem, s), FreeGroupElem)
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@test isa(Vector{FreeGroupElem}([s,t]), Vector{FreeGroupElem})
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@test length(FreeGroupElem(s)) == 1
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@test length(FreeGroupElem(t)) == 2
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end
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@testset "FreeGroup" begin
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@test isa(FreeGroup(["s", "t"]), AbstractAlgebra.Group)
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G = FreeGroup(["s", "t"])
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@testset "elements constructors" begin
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@test isa(G(), FreeGroupElem)
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@test eltype(G.gens) == Groups.FreeSymbol
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@test length(G.gens) == 2
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@test eltype(gens(G)) == FreeGroupElem
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@test length(gens(G)) == 2
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end
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s, t = gens(G)
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@testset "internal arithmetic" begin
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@test Vector{Groups.FreeGroupElem}([s,t]) == [Groups.GroupWord(s), Groups.GroupWord(t)]
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@test (s*s).symbols == (s^2).symbols
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@test hash([t^1,s^1]) == hash([t^2*inv(t),s*inv(s)*s])
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t_symb = Groups.FreeSymbol("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) == 0
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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 = FreeGroupElem([o.symbols..., p.symbols...])
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w.parent = G
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@test Groups.reduce!(w).symbols ==Vector{Groups.FreeSymbol}([])
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end
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@testset "Group 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, FreeGroupElem)
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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 = Groups.FreeSymbol("a")
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b = Groups.FreeSymbol("b")
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@test Groups.issubsymbol(a, Groups.change_pow(a,2)) == true
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@test Groups.issubsymbol(a, Groups.change_pow(a,-2)) == false
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@test Groups.issubsymbol(b, Groups.change_pow(a,-2)) == false
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@test Groups.issubsymbol(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{FreeGroupElem, FreeGroupElem}(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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G = FreeGroup(["x", "y"])
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x,y = gens(G)
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@test Groups.replace(x*y^9, 2, y^2, y) == x*y^8
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@test Groups.replace(x^3, 1, x^2, y) == x*y
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@test Groups.replace(y*x^3*y, 2, x^2, y) == y*x*y^2
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end
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end
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