fix bug with residues; close issue #605 (#606)

* fix bug with residues

* relax test

Author: jverzani

Project.toml

@@ -2,7 +2,7 @@ name = "Polynomials"
 uuid = "f27b6e38-b328-58d1-80ce-0feddd5e7a45"
 license = "MIT"
 author = "JuliaMath"
-version = "4.0.19"
+version = "4.0.20"
 
 [deps]
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"

src/rational-functions/common.jl

@@ -555,8 +555,9 @@ function residues(pq::AbstractRationalFunction; method=:numerical,  kwargs...)
             F = lowest_terms(r*(s-λₖ)^mₖ)
             rs = [F(λₖ)]
             j! = 1
+            dF = F
             for j ∈ 1:mₖ-1
-                dF = lowest_terms(derivative(F))
+                dF = lowest_terms(derivative(dF))
                 pushfirst!(rs, 1/j! * dF(λₖ))
                 j! *= (j+1)
             end

test/rational-functions.jl

@@ -124,6 +124,28 @@ end
     end
     @test norm(numerator(lowest_terms(d - pq)), Inf) <= sqrt(eps())
 
+    ## issue #605
+    s = x//1
+    X = 1//(s^4*(s+2))
+    _, r = residues(X)
+    Y = zero(s)
+    for (k,v) ∈ r
+        for (i,vᵢ) ∈ enumerate(v)
+            Y += vᵢ / (s-k)^i
+        end
+    end
+    @test X ≈ Y
+
+    X = 1//(s^3*(s+2))
+    _, r = residues(X)
+    Y = zero(s)
+    for (k,v) ∈ r
+        for (i,vᵢ) ∈ enumerate(v)
+            Y += vᵢ / (s-k)^i
+        end
+    end
+    @test X ≈ Y
+
 end
 
 @testset "As matrix elements" begin