confusion on the return of collect(permutation group)

[tthsqe12]

I have observed this behavior before and was wondering if it was intended:

julia> G = SymmetricGroup(3)
Full symmetric group over 3 elements

julia> collect(G)
6-element Vector{Perm{Int64}}:
 ()
 (1,2)
 (1,3,2)
 (2,3)
 (1,2,3)
 (1,3)

julia> Zx,x=ZZ["x"]; k,a=number_field(x^4+10x^2+2); G,_=galois_group(k)
(Group([ (1,2), (3,4), (1,3)(2,4) ]), Galois Context for x^4 + 10*x^2 + 2 and prime 11)

julia> collect(G)
8-element Vector{Any}:
 ()
 (3,4)
 (1,2)
 (1,2)(3,4)
 (1,3)(2,4)
 (1,3,2,4)
 (1,4,2,3)
 (1,4)(2,3)

The problem here is the Vector{Any} return type. It is my understanding that once this is the type of an object you cannot call methods declared like f(::Vector{PermGroupElem}) on it. Even more mysterious is that the following does get the correct array type:

julia> [g for g in G]
8-element Vector{PermGroupElem}:
 ()
 (3,4)
 (1,2)
 (1,2)(3,4)
 (1,3)(2,4)
 (1,3,2,4)
 (1,4,2,3)
 (1,4)(2,3)

[tthsqe12]

my package status:

(@v1.6) pkg> status
      Status `~/.julia/environments/v1.6/Project.toml`
  [c3fe647b] AbstractAlgebra v0.14.0
  [1f15a43c] CxxWrap v0.11.2
  [e30172f5] Documenter v0.26.3
  [3e1990a7] Hecke v0.9.6
  [7073ff75] IJulia v1.23.2
  [2edaba10] Nemo v0.21.0 `~/.julia/dev/Nemo`
  [f1435218] Oscar v0.5.2-DEV `~/.julia/dev/Oscar`
  [295af30f] Revise v3.1.14
  [bcd08a7b] Singular v0.4.7 `~/.julia/dev/Singular`
  [2913bbd2] StatsBase v0.33.3
  [43d676ae] Singular_jll v402.0.104+0
  [9a3f8284] Random
  [8dfed614] Test

[fingolfin]

SymmetricGroup is a command (or rather, type) from AbstractAlgebra, I think, and we are not really using it in Oscar (so we should not be exporting it -- that's a bug). There, use symmetric_group instead. With that, I get:

julia> G = symmetric_group(3)
Sym( [ 1 .. 3 ] )

julia> collect(G)
6-element Vector{Any}:
 ()
 (2,3)
 (1,3)
 (1,3,2)
 (1,2,3)
 (1,2)

Which is consistent with the output of galois_group, but of course the Any is still undesired.

To fix this, I think we must defined a suitable eltype method (perhaps there's a different / better way? Let me know, folks). Like this:

julia> Base.eltype(::Type{PermGroup}) = PermGroupElem

julia> collect(G)
6-element Vector{PermGroupElem}:
 ()
 (2,3)
 (1,3)
 (1,3,2)
 (1,2,3)
 (1,2)

@GDeFranceschi can you perhaps add such Base.eltypes methods for our various container types in the groups part of Oscar (groups, cosets, double cosets, GSets, ...) together with suitable tests (i.e., something like @test typeof(collect(G)) == Vector{PermGroupElem})

[GDeFranceschi]

For some of these already exists elem_type. For these types, do I just put eltype = elem_type?

[fingolfin]

Resolved:

julia> G = symmetric_group(3)
Sym( [ 1 .. 3 ] )

julia> collect(G)
6-element Vector{PermGroupElem}:
 ()
 (2,3)
 (1,3)
 (1,3,2)
 (1,2,3)
 (1,2)