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Groups.jl
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use tuples & domain in Automorphism evaluations

This commit is contained in:
kalmarek 2018-03-22 17:27:31 +01:00
parent 0233aedc41
commit 8f990d9014
1 changed files with 37 additions and 36 deletions
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73
test/AutGroup-tests.jl
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@ -15,71 +15,70 @@
end
a,b,c,d = Nemo.gens(FreeGroup(4))
domain = [a,b,c,d]
D = NTuple{4,FreeGroupElem}([a,b,c,d])
@testset "flip_autsymbol correctness" begin
@test Groups.flip_autsymbol(1)(domain) == [a^-1, b,c,d]
@test Groups.flip_autsymbol(2)(domain) == [a, b^-1,c,d]
@test Groups.flip_autsymbol(3)(domain) == [a, b,c^-1,d]
@test Groups.flip_autsymbol(4)(domain) == [a, b,c,d^-1]
@test inv(Groups.flip_autsymbol(1))(domain) == [a^-1, b,c,d]
@test inv(Groups.flip_autsymbol(2))(domain) == [a, b^-1,c,d]
@test inv(Groups.flip_autsymbol(3))(domain) == [a, b,c^-1,d]
@test inv(Groups.flip_autsymbol(4))(domain) == [a, b,c,d^-1]
@test Groups.flip_autsymbol(1)(deepcopy(D)) == (a^-1, b,c,d)
@test Groups.flip_autsymbol(2)(deepcopy(D)) == (a, b^-1,c,d)
@test Groups.flip_autsymbol(3)(deepcopy(D)) == (a, b,c^-1,d)
@test Groups.flip_autsymbol(4)(deepcopy(D)) == (a, b,c,d^-1)
@test inv(Groups.flip_autsymbol(1))(deepcopy(D)) == (a^-1, b,c,d)
@test inv(Groups.flip_autsymbol(2))(deepcopy(D)) == (a, b^-1,c,d)
@test inv(Groups.flip_autsymbol(3))(deepcopy(D)) == (a, b,c^-1,d)
@test inv(Groups.flip_autsymbol(4))(deepcopy(D)) == (a, b,c,d^-1)
end
@testset "perm_autsymbol correctness" begin
@test σ(domain) == domain
@test inv(σ)(domain) == domain
σ = Groups.perm_autsymbol([1,2,3,4])
@test σ(deepcopy(D)) == deepcopy(D)
@test inv(σ)(deepcopy(D)) == deepcopy(D)
@test σ(domain) == [b, c, d, a]
@test inv(σ)(domain) == [d, a, b, c]
σ = Groups.perm_autsymbol([2,3,4,1])
@test σ(deepcopy(D)) == (b, c, d, a)
@test inv(σ)(deepcopy(D)) == (d, a, b, c)
@test σ(domain) == [b, a, d, c]
@test inv(σ)(domain) == [b, a, d, c]
σ = Groups.perm_autsymbol([2,1,4,3])
@test σ(deepcopy(D)) == (b, a, d, c)
@test inv(σ)(deepcopy(D)) == (b, a, d, c)
@test σ(domain) == [b,c,a,d]
@test inv(σ)(domain) == [c,a,b,d]
σ = Groups.perm_autsymbol([2,3,1,4])
@test σ(deepcopy(D)) == (b, c, a, d)
@test inv(σ)(deepcopy(D)) == (c, a, b, d)
end
@testset "rmul/lmul_autsymbol correctness" begin
i,j = 1,2
r = Groups.rmul_autsymbol(i,j)
l = Groups.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]
@test r(deepcopy(D)) == (a*b, b, c, d)
@test inv(r)(deepcopy(D)) == (a*b^-1,b, c, d)
@test l(deepcopy(D)) == (b*a, b, c, d)
@test inv(l)(deepcopy(D)) == (b^-1*a,b, c, d)
i,j = 3,1
r = Groups.rmul_autsymbol(i,j)
l = Groups.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]
@test r(deepcopy(D)) == (a, b, c*a, d)
@test inv(r)(deepcopy(D)) == (a, b, c*a^-1,d)
@test l(deepcopy(D)) == (a, b, a*c, d)
@test inv(l)(deepcopy(D)) == (a, b, a^-1*c,d)
i,j = 4,3
r = Groups.rmul_autsymbol(i,j)
l = Groups.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]
@test r(deepcopy(D)) == (a, b, c, d*c)
@test inv(r)(deepcopy(D)) == (a, b, c, d*c^-1)
@test l(deepcopy(D)) == (a, b, c, c*d)
@test inv(l)(deepcopy(D)) == (a, b, c, c^-1*d)
i,j = 2,4
r = Groups.rmul_autsymbol(i,j)
l = Groups.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]
@test r(deepcopy(D)) == (a, b*d, c, d)
@test inv(r)(deepcopy(D)) == (a, b*d^-1,c, d)
@test l(deepcopy(D)) == (a, d*b, c, d)
@test inv(l)(deepcopy(D)) == (a, d^-1*b,c, d)
end
@testset "AutGroup/AutGroupElem constructors" begin
@ -149,8 +148,10 @@
@test a*b == b*a
@test a^3 * b^3 == A()
g,h = Nemo.gens(A)[[1,8]]
domain = Nemo.gens(A.objectGroup)
@test (g*h)(domain) == (h*g)(domain)
@test Groups.domain(A) == NTuple{4, FreeGroupElem}(gens(A.objectGroup))
@test (g*h)(Groups.domain(A)) == (h*g)(Groups.domain(A))
@test (g*h).savedhash != (h*g).savedhash
a = g*h
b = h*g