DefiniteIntegral and Multiplication in NormalizedPolynomialSpace (#64)

* DefiniteIntegral and Multiplication in NormalizedPolynomialSpace

* explicit test for DefiniteIntegral

* tests for isapproxhalfoddinteger

Author: jishnub

src/ApproxFunSingularities.jl

@@ -54,6 +54,8 @@ isapproxhalfoddinteger(::Integer) = false
 isequalminhalf(x) = x == -0.5
 isequalminhalf(::Integer) = false
 
+const MaybeNormalizedPolynomialSpace{S<:PolynomialSpace} = Union{S, NormalizedPolynomialSpace{S}}
+
 include("divide_singularity.jl")
 include("JacobiWeight.jl")
 include("JacobiWeightOperators.jl")

src/JacobiWeightOperators.jl

@@ -40,7 +40,7 @@ for (Func,Len) in ((:(Base.sum),:complexlength), (:linesum,:arclength))
                 return 0.5*$Len(d)*dotu(f.coefficients,c)
             end
         end
-        $Func(f::Fun{<:JacobiWeight{<:PolynomialSpace}}) =
+        $Func(f::Fun{<:JacobiWeight{<:MaybeNormalizedPolynomialSpace}}) =
             $Func(Fun(f,JacobiWeight(space(f).β, space(f).α, Chebyshev(domain(f)))))
     end
 end
@@ -219,7 +219,7 @@ function Multiplication(f::Fun, S::JacobiWeight)
     MultiplicationWrapper(f,SpaceOperator(M,S,rsp))
 end
 
-function Multiplication(f::Fun{<:JacobiWeight},S::PolynomialSpace)
+function Multiplication(f::Fun{<:JacobiWeight},S::MaybeNormalizedPolynomialSpace)
     M=Multiplication(Fun(space(f).space,f.coefficients),S)
     rsp=JacobiWeight(space(f).β,space(f).α,rangespace(M))
     MultiplicationWrapper(f,SpaceOperator(M,S,rsp))

test/runtests.jl

@@ -9,8 +9,10 @@ using ApproxFunBaseTest: testbandedoperator, testtransforms, testfunctional,
 using ApproxFunOrthogonalPolynomials
 using ApproxFunOrthogonalPolynomials: order
 using ApproxFunSingularities
-using LinearAlgebra
+using HalfIntegers
 using IntervalSets
+using LinearAlgebra
+using OddEvenIntegers
 using SpecialFunctions
 using Test
 
@@ -23,6 +25,13 @@ using Aqua
         project_toml_formatting = VERSION >= v"1.9")
 end
 
+@testset "utility function" begin
+    @test ApproxFunSingularities.isapproxhalfoddinteger(0.5)
+    @test ApproxFunSingularities.isapproxhalfoddinteger(half(1))
+    @test ApproxFunSingularities.isapproxhalfoddinteger(half(Odd(1)))
+    @test !ApproxFunSingularities.isapproxhalfoddinteger(1)
+end
+
 @testset "Sqrt" begin
     x=Fun(identity);
     @time @test sqrt(cos(π/2*x))(.1) ≈ sqrt(cos(.1π/2))
@@ -95,6 +104,10 @@ end
         x = Fun()
         M = Multiplication(x, JacobiWeight(0,0,Chebyshev()))
         @test exp(M).f == Multiplication(exp(x), Chebyshev()).f
+
+        g = Fun(x->√(1-x^2), JacobiWeight(0.5, 0.5, Jacobi(1,1)))
+        xg = Fun(x->x*√(1-x^2), JacobiWeight(0.5, 0.5, Jacobi(1,1)))
+        @test Multiplication(g) * Fun(NormalizedLegendre()) ≈ xg
     end
 
     @testset "Derivative" begin
@@ -492,6 +505,11 @@ end
             f = Fun(exp, S)
             @test convert(Number, B*f) ≈ sum(Fun(exp,domain(S)))
         end
+
+        f = Fun(x->√(1-x^2), JacobiWeight(0.5, 0.5, NormalizedJacobi(1,1)))
+        g = Fun(x->√(1-x^2), JacobiWeight(0.5, 0.5, Jacobi(1,1)))
+        @test sum(f) ≈ sum(g) ≈ π/2
+        @test DefiniteIntegral() * f ≈ DefiniteIntegral() * g ≈ π/2
     end
 end