Add setdiff for ElementarySpace

Author: lkdvos

src/spaces/cartesianspace.jl

@@ -56,4 +56,9 @@ flip(V::CartesianSpace) = V
 infimum(V₁::CartesianSpace, V₂::CartesianSpace) = CartesianSpace(min(V₁.d, V₂.d))
 supremum(V₁::CartesianSpace, V₂::CartesianSpace) = CartesianSpace(max(V₁.d, V₂.d))
 
+function Base.setdiff(V::CartesianSpace, W::CartesianSpace)
+    V ≿ W || throw(ArgumentError("$(W) is not a subspace of $(V)"))
+    return CartesianSpace(dim(V) - dim(W))
+end
+
 Base.show(io::IO, V::CartesianSpace) = print(io, "ℝ^$(V.d)")

src/spaces/complexspace.jl

@@ -69,4 +69,10 @@ function supremum(V₁::ComplexSpace, V₂::ComplexSpace)
            throw(SpaceMismatch("Supremum of space and dual space does not exist"))
 end
 
+function Base.setdiff(V::ComplexSpace, W::ComplexSpace)
+    (V ≿ W && isdual(V) == isdual(W)) ||
+        throw(ArgumentError("$(W) is not a subspace of $(V)"))
+    return ComplexSpace(dim(V) - dim(W), isdual(V))
+end
+
 Base.show(io::IO, V::ComplexSpace) = print(io, isdual(V) ? "(ℂ^$(V.d))'" : "ℂ^$(V.d)")

src/spaces/gradedspace.jl

@@ -187,6 +187,12 @@ function supremum(V₁::GradedSpace{I}, V₂::GradedSpace{I}) where {I<:Sector}
     end
 end
 
+function Base.setdiff(V::GradedSpace{I}, W::GradedSpace{I}) where {I<:Sector}
+    V ≿ W && isdual(V) == isdual(W) ||
+        throw(SpaceMismatch("$(W) is not a subspace of $(V)"))
+    return typeof(V)(c => dim(V, c) - dim(W, c) for c in sectors(V))
+end
+
 function Base.show(io::IO, V::GradedSpace{I}) where {I<:Sector}
     print(io, type_repr(typeof(V)), "(")
     seperator = ""

src/spaces/vectorspaces.jl

@@ -395,3 +395,11 @@ have the same value.
 function supremum(V₁::S, V₂::S, V₃::S...) where {S<:ElementarySpace}
     return supremum(supremum(V₁, V₂), V₃...)
 end
+
+"""
+    setdiff(V::ElementarySpace, W::ElementarySpace)
+
+Return the set difference of two elementary spaces, i.e. an instance `X::ElementarySpace`
+such that `V = W ⊕ X`.
+"""
+Base.setdiff(V₁::S, V₂::S) where {S<:ElementarySpace}