add TrivialMStructure <: MultiplicativeStructure + API

src/GroupRings.jl

@@ -565,7 +565,11 @@ end
 
 
 module New
+
 include("bases.jl")
+
+include("mstructures.jl")
+
 end
 
 end # of module GroupRings

src/mstructures.jl

@@ -0,0 +1,32 @@
+abstract type MultiplicativeStructure{Twisted,I} <: AbstractMatrix{I} end
+
+_istwisted(::MultiplicativeStructure{T}) where {T} = T
+_product(ms::MultiplicativeStructure, g, h) = _product(Val(_istwisted(ms)), g, h)
+
+_product(::Val{false}, g, h) = g * h
+_product(::Val{true}, g, h) = star(g) * h
+
+# ms::MultiplicativeStructure should implement:
+# * getindex(ms, i::Integer, j::Integer)
+# * size(ms)
+
+# additionally it may implement
+# * basis(ms)
+
+struct TrivialMStructure{Tw,I,B<:AbstractBasis} <: MultiplicativeStructure{Tw,I}
+    basis::B
+end
+
+TrivialMStructure{Tw}(basis::AbstractBasis{T,I}) where {Tw,T,I} =
+    TrivialMStructure{Tw,I,typeof(basis)}(basis)
+
+basis(mstr::TrivialMStructure) = mstr.basis
+Base.size(mstr::TrivialMStructure) = (l = length(basis(mstr)); (l, l))
+
+Base.@propagate_inbounds function Base.getindex(mstr::TrivialMStructure, i::Integer, j::Integer)
+    @boundscheck checkbounds(mstr, i, j)
+    b = basis(mstr)
+    g, h = b[i], b[j]
+    gh = _product(mstr, g, h)
+    return b[gh]
+end