coerce compatible jacobi to chebyshev/ultraspherical (#84)

Author: jishnub

src/Spaces/Jacobi/JacobiOperators.jl

@@ -495,7 +495,11 @@ function union_rule(A::Chebyshev,B::Jacobi)
             union(Jacobi(A),B)
         end
     else
-        NoSpace()
+        if isapprox(B.a,-0.5) && isapprox(B.b,-0.5)
+            union(A, Chebyshev(domain(B)))
+        else
+            NoSpace()
+        end
     end
 end
 function union_rule(A::Ultraspherical,B::Jacobi)
@@ -508,7 +512,11 @@ function union_rule(A::Ultraspherical,B::Jacobi)
             union(Jacobi(A),B)
         end
     else
-        NoSpace()
+        if isapprox(B.a,m-0.5) && isapprox(B.b,m-0.5)
+            union(A, Ultraspherical(m, domain(B)))
+        else
+            NoSpace()
+        end
     end
 end
 

test/JacobiTest.jl

@@ -171,6 +171,10 @@ import ApproxFunOrthogonalPolynomials: jacobip
         @test !hasconversion(a,b)
 
         @testset for a in Any[Chebyshev(0..1), Ultraspherical(1, 0..1)]
+            b = Jacobi(a)
+            c = union(a, b)
+            @test c == a
+
             b = ApproxFunBase.setdomain(Jacobi(a), 1..2)
             c = union(a, b)
             d = domain(c)
@@ -184,6 +188,11 @@ import ApproxFunOrthogonalPolynomials: jacobip
             @test 0 in d
             @test 1 in d
             @test 2 in d
+
+            b = Legendre(domain(a))
+            c = union(a, b)
+            d = domain(c)
+            @test d == domain(a)
         end
     end