TODO list

[kalmarek]

• [x] finite fields
• [x] eigenspaces (nullspace, etc)
• [x] es decomposition
• [x] Dixon over finite fields
• [x] Cyclotomics lift to C

[tweisser]

If we define a structure for echelonized subspaces as I did here, we can get rid of the function to get the right columns of the refinement matrix.

[tweisser]

At the moment the refine function creates a new ESD

function refine(esd::EigenSpaceDecomposition{T}, M::Matrix{T}) where T
    nbasis = Array{T}(undef, 0, size(first(esd), 2))
    nptrs = [1]
    for (i, e) in enumerate(esd)
        if size(e, 1) > 1
            esd2, ptrs = eigen_decomposition!(e*M[:, _find_l(e)])
            nbasis = vcat(nbasis, esd2*e)
            append!(nptrs, ptrs.+(pop!(nptrs)-1))
        else
            nbasis = vcat(nbasis, e)
            push!(nptrs, nptrs[end]+1)
        end
    end
    return EigenSpaceDecomposition(nbasis,nptrs)
end

[tweisser]

I cannot make these line work:

using AbstractAlgebra
using PermutationGroups

G = SymmetricGroup(4)
S = gens(G)
ccG = conjugacy_classes(G)

AbstractAlgebra is on version 0.9.2 PermutationGroups checked out for dev on master

[kalmarek]

with latest PermutationGroups this should work

julia> using AbstractAlgebra, PermutationGroups
[ Info: Precompiling PermutationGroups [8bc5a954-2dfc-11e9-10e6-cd969bffa420]

julia> G = SymmetricGroup(4)
Full symmetric group over 4 elements

julia> S = gens(G)
2-element Array{Perm{Int64},1}:
 (1,2)
 (1,2,3,4)

julia> ccG = conjugacy_classes(G)
5-element Array{PermutationGroups.Orbit1{Perm{Int64},Nothing},1}:
 PermutationGroups.Orbit1{Perm{Int64},Nothing}(Perm{Int64}[()], Dict{Perm{Int64},Nothing}(() => nothing))
 PermutationGroups.Orbit1{Perm{Int64},Nothing}(Perm{Int64}[(1,2), (2,3), (1,3), (3,4), (2,4), (1,4)], Dict{Perm{Int64},Nothing}((2,3) => nothing,(1,3) => nothing,(3,4) => nothing,(1,4) => nothing,(1,2) => nothing,(2,4) => nothing))
 PermutationGroups.Orbit1{Perm{Int64},Nothing}(Perm{Int64}[(1,3,2), (1,2,3), (2,4,3), (2,3,4), (1,4,3), (1,3,4), (1,4,2), (1,2,4)], Dict{Perm{Int64},Nothing}((2,3,4) => nothing,(2,4,3) => nothing,(1,2,4) => nothing,(1,3,4) => nothing,(1,3,2) => nothing,(1,4,2) => nothing,(1,4,3) => nothing,(1,2,3) => nothing))
 PermutationGroups.Orbit1{Perm{Int64},Nothing}(Perm{Int64}[(1,2,4,3), (1,4,3,2), (1,4,2,3), (1,3,2,4), (1,3,4,2), (1,2,3,4)], Dict{Perm{Int64},Nothing}((1,2,3,4) => nothing,(1,3,2,4) => nothing,(1,4,2,3) => nothing,(1,3,4,2) => nothing,(1,4,3,2) => nothing,(1,2,4,3) => nothing))
 PermutationGroups.Orbit1{Perm{Int64},Nothing}(Perm{Int64}[(1,2)(3,4), (1,4)(2,3), (1,3)(2,4)], Dict{Perm{Int64},Nothing}((1,2)(3,4) => nothing,(1,4)(2,3) => nothing,(1,3)(2,4) => nothing))

I needed to clean-up

[tweisser]

Someone should increase code coverage before we go on...

[kalmarek]

thanks for the nudge ;)