implicit ultraspherical order from Jacobi (#883)

* implicit ultraspherical order from Jacobi

* ConcreteConversion instead of Conversion

Author: jishnub

Project.toml

@@ -1,6 +1,6 @@
 name = "ApproxFun"
 uuid = "28f2ccd6-bb30-5033-b560-165f7b14dc2f"
-version = "0.13.19"
+version = "0.13.20"
 
 [deps]
 AbstractFFTs = "621f4979-c628-5d54-868e-fcf4e3e8185c"

src/ApproxFun.jl

@@ -23,7 +23,7 @@ import ApproxFunBase: Fun, UnsetSpace, VFun, UnivariateSpace, SumSpace, Space,
                     isapproxinteger, components, promotedomainspace, choosedomainspace,
                     AbstractProductSpace, MultivariateFun, BivariateSpace,
                     @calculus_operator, slnorm, sample, chop!, 𝒟, ∫, ⨜, ⨍,
-                    InterlaceOperator_Diagonal, eigs
+                    InterlaceOperator_Diagonal, eigs, ConcreteConversion
 
 export ∫, ⨜, ⨍, 𝒟
 

src/Extras/fractional.jl

@@ -29,14 +29,13 @@ end
 function LeftIntegral(S::Ultraspherical,k)
     J = Jacobi(S)
     LI = LeftIntegral(J,k)
-    LeftIntegralWrapper(LI*Conversion(S,J),0.5,S,rangespace(LI))
+    LeftIntegralWrapper(LI*ConcreteConversion(S,J),0.5,S,rangespace(LI))
 end
 
 function LeftIntegral(S::Chebyshev,k)
-    LI = LeftIntegral(Ultraspherical(1//2,domain(S)),k)
-    LeftIntegralWrapper(
-        LI*Conversion(S,Ultraspherical(1//2,domain(S))),
-            0.5,S,rangespace(LI))
+    SU = Ultraspherical(Legendre(domain(S)))
+    LI = LeftIntegral(SU,k)
+    LeftIntegralWrapper(LI*ConcreteConversion(S,SU),0.5,S,rangespace(LI))
 end