83 lines
2.2 KiB
Julia
83 lines
2.2 KiB
Julia
###############################################################################
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#
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# Orbits and orbit_spvector
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#
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###############################################################################
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function orbit_decomposition(G::Group, E::Vector, rdict=GroupRings.reverse_dict(E))
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elts = collect(elements(G))
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tovisit = trues(E);
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orbits = Vector{Vector{Int}}()
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orbit = zeros(Int, length(elts))
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for i in 1:endof(E)
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if tovisit[i]
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g = E[i]
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Threads.@threads for j in 1:length(elts)
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orbit[j] = rdict[elts[j](g)]
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end
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tovisit[orbit] = false
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push!(orbits, unique(orbit))
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end
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end
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return orbits
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end
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function orbit_spvector(vect::AbstractVector, orbits)
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orb_vector = spzeros(length(orbits))
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for (i,o) in enumerate(orbits)
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k = vect[collect(o)]
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val = k[1]
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@assert all(k .== val)
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orb_vector[i] = val
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end
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return orb_vector
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end
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###############################################################################
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#
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# perm-, matrix-, representations
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#
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###############################################################################
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function perm_repr(g::GroupElem, E::Vector, E_dict)
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p = Vector{Int}(length(E))
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for (i,elt) in enumerate(E)
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p[i] = E_dict[g(elt)]
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end
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return p
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end
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function perm_reps(G::Group, E::Vector, E_rdict=GroupRings.reverse_dict(E))
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elts = collect(elements(G))
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l = length(elts)
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preps = Vector{perm}(l)
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permG = PermutationGroup(length(E))
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Threads.@threads for i in 1:l
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preps[i] = permG(PropertyT.perm_repr(elts[i], E, E_rdict), false)
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end
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return Dict(elts[i]=>preps[i] for i in 1:l)
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end
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function matrix_repr(x::GroupRingElem, mreps::Dict)
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nzeros = findn(x.coeffs)
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return sum(x[i].*mreps[parent(x).basis[i]] for i in nzeros)
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end
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function matrix_reps(preps::Dict{T,perm{I}}) where {T<:GroupElem, I<:Integer}
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kk = collect(keys(preps))
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mreps = Vector{SparseMatrixCSC{Float64, Int}}(length(kk))
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Threads.@threads for i in 1:length(kk)
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mreps[i] = AbstractAlgebra.matrix_repr(preps[kk[i]])
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end
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return Dict(kk[i] => mreps[i] for i in 1:length(kk))
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end
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