Addition of LazyTensor and LazySum

[mabuni1998]

The current implementation for +(a::LazyTensor,b::LazyTensor) does not allow operators acting on different spaces. See the following:

julia>b = FockBasis(2);

julia> a = destroy(b);

julia> LazyTensor(b⊗b,[1,2],(a,a))+LazyTensor(b⊗b,[1,2],(a,a))
ERROR: ArgumentError: Addition of LazyTensor operators is only defined in case both operators act nontrivially on the same, single tensor factor.
Stacktrace:
 [1] +(a::LazyTensor{CompositeBasis{Vector{Int64}, Tuple{FockBasis{Int64}, FockBasis{Int64}}}, CompositeBasis{Vector{Int64}, Tuple{FockBasis{Int64}, FockBasis{Int64}}}, ComplexF64, Vector{Int64}, Tuple{Operator{FockBasis{Int64}, FockBasis{Int64}, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, Operator{FockBasis{Int64}, FockBasis{Int64}, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}}}, b::LazyTensor{CompositeBasis{Vector{Int64}, Tuple{FockBasis{Int64}, FockBasis{Int64}}}, CompositeBasis{Vector{Int64}, Tuple{FockBasis{Int64}, FockBasis{Int64}}}, ComplexF64, Vector{Int64}, Tuple{Operator{FockBasis{Int64}, FockBasis{Int64}, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, Operator{FockBasis{Int64}, FockBasis{Int64}, SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}}})
   @ QuantumOpticsBase C:\Users\Matias\.julia\packages\QuantumOpticsBase\tj3Ta\src\operators_lazytensor.jl:102
 [2] top-level scope
   @ REPL[5]:1

One could create a LazySum operator of the two LazyTensor objects, something like:

function Base.:+(op1::LazyTensor{B1,B2},op2::LazyTensor{B1,B2}) where {B1,B2}
    LazySum(op1,op2)
end

Similarly, one could add:

function Base.:+(op1::LazySum{B1,B2},op2::LazyTensor{B1,B2}) where {B1,B2}
    op1+LazySum(op2)
end

Is there a reason this is not a good idea?

[amilsted]

Think we have this now?