isconvertible returns true for same space, union of Fourier and Cheby…

…shev gives a Chebyshev (#602)

src/Fun/Space.jl

@@ -291,7 +291,7 @@ hasconversion(a,b) = maxspace(a,b) == b
 
 
 # tests whether a coefficients can be converted to b
-isconvertible(a,b) = hasconversion(a,b)
+isconvertible(a,b) = a == b || hasconversion(a,b)
 
 ## Conversion routines
 #       coefficients(v::AbstractVector,a,b)

src/Spaces/Modifier/SumSpace.jl

@@ -270,7 +270,7 @@ function union_rule(B::ConstantSpace,A::SumSpace)
     end
 end
 
-function union_rule(A::SumSpace,B::Space)
+function union_rule(A::SumSpace, B::Space)
     if !domainscompatible(A,B)
         NoSpace()
     else
@@ -283,6 +283,9 @@ function union_rule(A::SumSpace,B::Space)
     end
 end
 
+union_rule(A::SumSpace{<:Any,<:PeriodicInterval}, B::Space{<:IntervalDomain}) =
+    union(Space(Interval(domain(A))), B)
+
 
 ## components
 

src/Spaces/PeriodicSpace.jl

@@ -14,3 +14,5 @@ DefiniteIntegral(d::PeriodicDomain) = DefiniteIntegral(Laurent(d))
 DefiniteLineIntegral(d::PeriodicDomain) = DefiniteLineIntegral(Laurent(d))
 
 ## Toeplitz
+union_rule(A::Space{<:PeriodicInterval}, B::Space{<:IntervalDomain}) =
+    union(Space(Interval(domain(A))), B)

test/SpacesTest.jl

@@ -329,13 +329,11 @@ using ApproxFun, SpecialFunctions, LinearAlgebra, Test
         @test o(0.5) == 1
     end
 
-
     @testset "blockbandinds for FiniteOperator of pointscompatibleace bug" begin
         S = ApproxFun.PointSpace([1.0,2.0])
         @test ApproxFun.blockbandinds(FiniteOperator([1 2; 3 4],S,S)) == (0,0)
     end
 
-    #SumSpace Conversion
     @testset "SumSpace Conversion" begin
         H = ApproxFun.HeavisideSpace([-1.0,0.0,1.0])
         C = ApproxFun.ContinuousSpace(ApproxFun.PiecewiseSegment([-1.0,0,1]))
@@ -354,4 +352,21 @@ using ApproxFun, SpecialFunctions, LinearAlgebra, Test
         f = Fun(S, randn(100))
         @test (Conversion(S,S2) * f)(0.1) ≈ f(0.1)
     end
+
+    @testset "Mix Fourier-Chebyshev (#602)" begin
+        s = Chebyshev(-π..π)
+        a = Fun(t-> 1+sin(cos(2t)), s)
+        L = Derivative() + a
+        f = Fun(t->exp(sin(10t)), s)
+        B = periodic(s,0)
+        uChebyshev = [B;L] \ [0.;f]
+
+        s = Fourier(-π..π)
+        a = Fun(t-> 1+sin(cos(2t)), s)
+        L = Derivative() + a
+        f = Fun(t->exp(sin(10t)), s)
+        uFourier = L\f
+
+        @test norm(uFourier-uChebyshev) ≤ 100eps()
+    end
 end