tests for derivative in normalized spaces (#174)

* tests for derivative in normalized spaces

* remove unnecessary type assertions

Author: jishnub

src/Operators/general/algebra.jl

@@ -399,9 +399,9 @@ for TYP in (:Matrix, :BandedMatrix, :RaggedMatrix)
         # for large k its upper triangular
         RT = $TYP{T}
         RT2 = _rettype(RT)
-        BA::RT2 = strictconvert(RT, P.ops[end][krl[end,1]:krl[end,2],jr])::RT
+        BA::RT2 = strictconvert(RT, P.ops[end][krl[end,1]:krl[end,2],jr])
         for m = (length(P.ops)-1):-1:1
-            BA = strictconvert(RT, P.ops[m][krl[m,1]:krl[m,2],krl[m+1,1]:krl[m+1,2]])::RT * BA
+            BA = strictconvert(RT, P.ops[m][krl[m,1]:krl[m,2],krl[m+1,1]:krl[m+1,2]]) * BA
         end
 
         RT(BA)::RT2

test/SpacesTest.jl

@@ -343,14 +343,16 @@ using BandedMatrices: rowrange, colrange
             for d in Any[(), (0..1,)]
                 for ST in Any[Chebyshev, Legendre,
                         (x...) -> Jacobi(2,2,x...), (x...) -> Jacobi(1.5,2.5,x...)]
-                    S = ST(d...)
-                    @test Derivative(S) == Derivative(S,1)
-                    @test Derivative(S)^2 == Derivative(S,2)
-                    f = Fun(x->x^3, S)
-                    @test Derivative(S) * f ≈ Fun(x->3x^2, S)
-                    @test Derivative(S,2) * f ≈ Fun(x->6x, S)
-                    @test Derivative(S,3) * f ≈ Fun(x->6, S)
-                    @test Derivative(S,4) * f ≈ zeros(S)
+                    S1 = ST(d...)
+                    for S in [S1, NormalizedPolynomialSpace(S1)]
+                        @test Derivative(S) == Derivative(S,1)
+                        @test Derivative(S)^2 == Derivative(S,2)
+                        f = Fun(x->x^3, S)
+                        @test Derivative(S) * f ≈ Fun(x->3x^2, S)
+                        @test Derivative(S,2) * f ≈ Fun(x->6x, S)
+                        @test Derivative(S,3) * f ≈ Fun(x->6, S)
+                        @test Derivative(S,4) * f ≈ zeros(S)
+                    end
                 end
             end
             @test Derivative(Chebyshev()) != Derivative(Chebyshev(), 2)