Add key_type

src/bases.jl

@@ -14,6 +14,12 @@ Base.eltype(b::AbstractBasis) = eltype(typeof(b))
 Base.keytype(::Type{<:AbstractBasis{T,I}}) where {T,I} = I
 Base.keytype(b::AbstractBasis) = keytype(typeof(b))
 
+key_type(b) = keytype(b)
+# `keytype(::Type{SparseVector{V,K}})` is not defined so it falls
+# back to `keytype{::Type{<:AbstractArray})` which returns `Int`.
+key_type(::Type{SparseArrays.SparseVector{V,K}}) where {V,K} = K
+key_type(v::SparseArrays.SparseVector) = key_type(typeof(v))
+
 """
     ImplicitBasis{T,I}
 Implicit bases are not stored in memory and can be potentially infinite.

src/types.jl

@@ -44,10 +44,10 @@ struct AlgebraElement{A,T,V} <: MA.AbstractMutable
 end
 
 function _sanity_checks(coeffs, A::AbstractStarAlgebra)
-    @assert keytype(coeffs) == keytype(basis(A))
+    @assert key_type(coeffs) == keytype(basis(A))
 end
 function _sanity_checks(coeffs::AbstractVector, A::AbstractStarAlgebra)
-    @assert keytype(coeffs) == keytype(basis(A))
+    @assert key_type(coeffs) == keytype(basis(A))
     @assert Base.haslength(basis(A))
     @assert length(coeffs) == length(basis(A))
 end