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fix too restrictive method installations #4149

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Sep 26, 2024
Merged

fix too restrictive method installations #4149

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1a8ec62
fix too restrictive method installations
ThomasBreuer Sep 24, 2024
2e4b498
fix signatures
ThomasBreuer Sep 24, 2024
cab15f2
next round
ThomasBreuer Sep 25, 2024
c8451b9
address comments (improve syntax)
ThomasBreuer Sep 26, 2024
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4 changes: 2 additions & 2 deletions docs/src/Groups/autgroup.md
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Expand Up @@ -11,8 +11,8 @@ automorphism_group(G::GAPGroup)

The following functions are available for automorphisms, some of them similar to the corresponding functions for homomorphisms of groups.
```@docs
is_invariant(f::GAPGroupElem{AutomorphismGroup{T}}, H::T) where T<:GAPGroup
restrict_automorphism(f::GAPGroupElem{AutomorphismGroup{T}}, H::T, A=automorphism_group(H)) where T <: GAPGroup
is_invariant(f::GAPGroupElem{AutomorphismGroup{T}}, H::GAPGroup) where T <: GAPGroup
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restrict_automorphism(f::GAPGroupElem{AutomorphismGroup{T}}, H::GAPGroup, A=automorphism_group(H)) where T <: GAPGroup
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induced_automorphism(f::GAPGroupHomomorphism, mH::GAPGroupHomomorphism)
hom(x::GAPGroupElem{AutomorphismGroup{T}}) where T <: GAPGroup
```
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15 changes: 7 additions & 8 deletions src/Groups/homomorphisms.jl
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Expand Up @@ -231,8 +231,7 @@ end


"""
is_invariant(f::GAPGroupHomomorphism, H::Group)
is_invariant(f::GAPGroupElem{AutomorphismGroup{T}}, H::T)
is_invariant(f::GAPGroupHomomorphism, H::GAPGroup)

Return whether `f(H) == H` holds.
An exception is thrown if `domain(f)` and `codomain(f)` are not equal
Expand Down Expand Up @@ -1298,7 +1297,7 @@ end
Base.:^(x::GAPGroupElem{T},f::GAPGroupElem{AutomorphismGroup{T}}) where T <: GAPGroup = apply_automorphism(f, x, true)
#Base.:^(f::GAPGroupElem{AutomorphismGroup{T}},g::GAPGroupElem{AutomorphismGroup{T}}) where T <: GAPGroup = g^-1*f*g

function (A::AutomorphismGroup{T})(f::GAPGroupHomomorphism{T,T}) where T <: GAPGroup
function (A::AutomorphismGroup{<: GAPGroup})(f::GAPGroupHomomorphism{T,T}) where T <: GAPGroup
@assert domain(f)==A.G && codomain(f)==A.G "f not in A"
@assert is_bijective(f) "f not in A"
return group_element(A, GapObj(f))
Expand Down Expand Up @@ -1351,11 +1350,11 @@ function inner_automorphism_group(A::AutomorphismGroup{T}) where T <: GAPGroup
end

"""
is_invariant(f::GAPGroupElem{AutomorphismGroup{T}}, H::T)
is_invariant(f::GAPGroupElem{AutomorphismGroup{T}}, H::GAPGroup) where T <: GAPGroup

Return whether `f`(`H`) == `H`.
"""
function is_invariant(f::GAPGroupElem{AutomorphismGroup{T}}, H::T) where T<:GAPGroup
function is_invariant(f::GAPGroupElem{AutomorphismGroup{T}}, H::GAPGroup) where T <: GAPGroup
@assert GAPWrap.IsSubset(GapObj(parent(f).G), GapObj(H)) "Not a subgroup of the domain"
return GAPWrap.Image(GapObj(f), GapObj(H)) == GapObj(H)
end
Expand All @@ -1379,18 +1378,18 @@ end
induced_automorphism(f::GAPGroupHomomorphism, mH::GAPGroupElem{AutomorphismGroup{T}}) where T <: GAPGroup = induced_automorphism(f,hom(mH))

"""
restrict_automorphism(f::GAPGroupElem{AutomorphismGroup{T}}, H::T)
restrict_automorphism(f::GAPGroupElem{AutomorphismGroup{T}}, H::GAPGroup) where T <: GAPGroup

Return the restriction of `f` to `H` as an automorphism of `H`.
An exception is thrown if `H` is not invariant under `f`.
"""
function restrict_automorphism(f::GAPGroupElem{AutomorphismGroup{T}}, H::T, A=automorphism_group(H)) where T <: GAPGroup
function restrict_automorphism(f::GAPGroupElem{AutomorphismGroup{T}}, H::GAPGroup, A=automorphism_group(H)) where T <: GAPGroup
@assert is_invariant(f,H) "H is not invariant under f!"
fh = hom(H, H, gens(H), [f(x) for x in gens(H)], check = false)
return A(fh)
end

function restrict_homomorphism(f::GAPGroupElem{AutomorphismGroup{T}}, H::T) where T <: GAPGroup
function restrict_homomorphism(f::GAPGroupElem{AutomorphismGroup{T}}, H::GAPGroup) where T <: GAPGroup
return restrict_homomorphism(hom(f),H)
end

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2 changes: 1 addition & 1 deletion src/Groups/libraries/smallgroups.jl
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Expand Up @@ -83,7 +83,7 @@ Pc group of order 60
```
"""
function small_group(::Type{T}, n::IntegerUnion, m::IntegerUnion) where T
G = _small_group(n, m)
G = small_group(n, m)
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return T(G)
end

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3 changes: 1 addition & 2 deletions src/Groups/sub.jl
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Expand Up @@ -33,8 +33,7 @@ julia> H == alternating_group(4)
true
```
"""
function sub(G::GAPGroup, gens::AbstractVector{S}; check::Bool = true) where S <: GAPGroupElem
@assert elem_type(G) == S
function sub(G::GAPGroup, gens::AbstractVector{<: GAPGroupElem}; check::Bool = true)
if check
@req all(x -> parent(x) === G || x in G, gens) "not all elements of gens lie in G"
end
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129 changes: 68 additions & 61 deletions test/Groups/homomorphisms.jl
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Expand Up @@ -656,69 +656,76 @@ end
test_kernel(G,H,f)
end

@testset "Automorphism group of Sym(n)" begin
G=symmetric_group(4)
A=automorphism_group(G)

@test A isa AutomorphismGroup
@test A isa AutomorphismGroup{PermGroup}
@test A.G == G
@test is_isomorphic(G,A)
@test order(A) == 24
@test A==inner_automorphism_group(A)[1]

f = rand(A)
g = rand(A)
x = rand(G)
o = order(f)
fh = hom(f)
@test f isa Oscar.GAPGroupElem{typeof(A)}
@test fh isa Oscar.GAPGroupHomomorphism{PermGroup,PermGroup}
@test A(fh)==f
@test f(x)==x^f
@test f^o == one(A)
@test f*f^-1 == one(A)
@test (f*g)(x) == g(f(x))
@test comm(f,g) == f^-1*g^-1*f*g
@test f(G[1])==fh(G[1])
@test f(G[2])==fh(G[2])
alt = alternating_group(4)
N,e = sub(G,[alt[1],alt[2]])
@test e*f==e*fh
@testset "Automorphism group of a perm. group or a (sub) pc group" begin
for T in [PermGroup, PcGroup, SubPcGroup]
G = small_group(T, 24, 12)
A = automorphism_group(G)

@test A isa AutomorphismGroup
@test A isa AutomorphismGroup{T}
@test A.G === G
@test is_isomorphic(G, A)
@test order(A) == 24
@test A == inner_automorphism_group(A)[1]

f = rand(A)
g = rand(A)
x = rand(G)
o = order(f)
fh = hom(f)
@test f isa Oscar.GAPGroupElem{typeof(A)}
@test fh isa Oscar.GAPGroupHomomorphism{T, T}
@test A(fh) == f
@test f(x) == x^f
@test f^o == one(A)
@test f*f^-1 == one(A)
@test (f*g)(x) == g(f(x))
@test comm(f, g) == f^-1*g^-1*f*g
@test f(G[1]) == fh(G[1])
@test f(G[2]) == fh(G[2])
H = derived_subgroup(G)[1]
N, e = sub(G, [H[1], H[2]])
@test e*f == e*fh

C = cyclic_group(2) # type is independent of `T`
oC = one(C)
gC = gen(C, 1)
g = hom(G, C, x -> x in H ? oC : gC)
@test f*g == fh*g
@test kernel(f*g) == kernel(g)
@test induced_automorphism(g, f) == induced_automorphism(g, fh)

@test is_inner_automorphism(f)
g1 = inner_automorphism(G(H[1]))
@test !(g in A)
g1 = A(g1)
@test g1 in A
g2 = A(inner_automorphism(G(H[2])))
AA, phi = sub(A, [g1, g2])
@test is_isomorphic(AA, H)
@test index(A, AA) == 2
@test is_normal_subgroup(AA, A)
@test is_normalized_by(AA, A)
@test phi(AA[1]) == AA[1]
@test phi(AA[2]) == AA[2]
@test order(quo(A, AA)[1]) == 2
@test is_invariant(f, H)

S = sylow_subgroup(G, 3)[1]
x = gen(S, 1)
f = A(hom(G, G, y -> y^x))
fHa = restrict_automorphism(f, H)
fHh = restrict_homomorphism(f, H)
@test parent(fHa) == automorphism_group(H)
@testset for g in gens(H)
@test fHa(g) == H(f(g))
@test fHh(g) == H(f(g))
end

C=cyclic_group(2)
g = hom(G,C,x -> C[1]^((1-sign(x))÷2) )
@test f*g == fh*g
@test kernel(f*g)==kernel(g)

@test is_inner_automorphism(f)
g1 = inner_automorphism(G(alt[1]))
@test !(g in A)
g1 = A(g1)
@test g1 in A
g2 = A(inner_automorphism(G(alt[2])))
AA,phi = sub(A,[g1,g2])
@test is_isomorphic(AA,alt)
@test index(A,AA)==2
@test is_normal_subgroup(AA, A)
@test is_normalized_by(AA, A)
@test phi(AA[1])==AA[1]
@test phi(AA[2])==AA[2]
@test order(quo(A,AA)[1])==2
@test is_invariant(f,alt)

H = alternating_group(4)
x = cperm(G,[1,2,3])
f = A(hom(G,G,y->y^x))
fa = restrict_automorphism(f,H)
@test parent(fa)==automorphism_group(H)
@testset for g in gens(H)
@test fa(g)==H(f(g))
V, _ = pcore(G, 2)
S, g = quo(G, V)
@test induced_automorphism(g, f) == automorphism_group(S)(inner_automorphism(g(x)))
end

S = symmetric_group(3)
g = hom(G,S,[cperm([1,2,3,4]), cperm([1,2])], [cperm([1,3]), cperm([1,2])])
@test induced_automorphism(g,f)==automorphism_group(S)(inner_automorphism(cperm(S,[1,2,3])))
end

@testset "Other automorphisms groups" begin
Expand Down
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