implement minimal Basis struct

src/GroupRings.jl

@@ -563,4 +563,9 @@ function initializepm!(RG::GroupRing; fill::Bool=false)
    return RG
 end
 
+
+module New
+include("bases.jl")
+end
+
 end # of module GroupRings

src/bases.jl

@@ -0,0 +1,26 @@
+abstract type AbstractBasis{T,I} <: AbstractVector{T} end
+
+struct Basis{T,I,A<:AbstractVector{T}} <: AbstractBasis{T,I}
+    basis::A
+    rbasis::Dict{T,I}
+end
+
+function Basis{I}(basis::AbstractVector) where I
+    length(basis) <= typemax(I) ||
+        throw("index type $I is to small for basis of length $(length(basis))")
+    @assert !(eltype(basis) <: Integer)
+    return Basis(basis, Dict(b => I(idx) for (idx, b) in pairs(basis)))
+end
+
+Base.size(b::Basis) = size(b.basis)
+
+Base.IndexStyle(::Type{<:Basis{T,I,A}}) where {T,I,A} = Base.IndexStyle(A)
+
+Base.@propagate_inbounds Base.getindex(b::Basis, i::Integer) = b.basis[i]
+Base.@propagate_inbounds Base.getindex(b::Basis{T}, g::T) where {T} = b.rbasis[g]
+
+Base.in(g, b::Basis) = haskey(b.rbasis, g)
+
+## are these really that useful?
+SparseArrays.indtype(::Type{<:Basis{T,I}}) where {T,I} = I
+SparseArrays.indtype(b::Basis) = SparseArrays.indtype(typeof(b))