Reduce cost of weighted lowering (#87)

* more direct constant computation

* Update Project.toml

Author: TSGut

Project.toml

@@ -1,7 +1,7 @@
 name = "SemiclassicalOrthogonalPolynomials"
 uuid = "291c01f3-23f6-4eb6-aeb0-063a639b53f2"
 authors = ["Sheehan Olver <[email protected]>"]
-version = "0.5"
+version = "0.5.1"
 
 [deps]
 ArrayLayouts = "4c555306-a7a7-4459-81d9-ec55ddd5c99a"

src/SemiclassicalOrthogonalPolynomials.jl

@@ -349,7 +349,7 @@ function \(w_A::WeightedSemiclassicalJacobi, w_B::WeightedSemiclassicalJacobi)
     Δc = B.c-A.c
 
     if (wA.a == A.a) && (wA.b == A.b) && (wA.c == A.c) && (wB.a == B.a) && (wB.b == B.b) && (wB.c == B.c) && isinteger(A.a) && isinteger(A.b) && isinteger(A.c) && isinteger(B.a) && isinteger(B.b) && isinteger(B.c)
-        k = (A \ SemiclassicalJacobiWeight(A.t,Δa,Δb,Δc))[1]
+        k = sum(SemiclassicalJacobiWeight(B.t,B.a,B.b,B.c))/sum(SemiclassicalJacobiWeight(A.t,A.a,A.b,A.c)) # = (A \ SemiclassicalJacobiWeight(A.t,Δa,Δb,Δc))[1]
         return (ApplyArray(*,Diagonal(Fill(k,∞)),(B \ A)))'
     elseif wA.a == wB.a && wA.b == wB.b && wA.c == wB.c # fallback to Christoffel–Darboux
         A \ B
@@ -508,4 +508,4 @@ end
 
 include("neg1c.jl")
 
-end
+end