Fix differentiation of zero polynomial

Author: blegat

src/differentiation.jl

@@ -37,7 +37,15 @@ differentiate(α::T, v::AbstractVariable) where T = zero(T)
 differentiate(v1::AbstractVariable, v2::AbstractVariable) = v1 == v2 ? 1 : 0
 differentiate(t::AbstractTermLike, v::AbstractVariable) = coefficient(t) * differentiate(monomial(t), v)
 # The polynomial function will take care of removing the zeros
-differentiate(p::APL, v::AbstractVariable) = polynomial!(differentiate.(terms(p), v), SortedState())
+function differentiate(p::APL, v::AbstractVariable)
+    if iszero(p)
+        # As `terms(p)` is empty, `differentiate.(terms(p), v)` gives `Any[]`.
+        T = typeof(differentiate(one(termtype(p)), v))
+        polynomial!(T[], SortedUniqState())
+    else
+        polynomial!(differentiate.(terms(p), v), SortedState())
+    end
+end
 differentiate(p::RationalPoly, v::AbstractVariable) = (differentiate(p.num, v) * p.den - p.num * differentiate(p.den, v)) / p.den^2
 
 const ARPL = Union{APL, RationalPoly}

test/differentiation.jl

@@ -38,6 +38,12 @@
     @test differentiate(f, [x, y, z]) == [2x 1 0; 4 0 2z]
     @test differentiate(f, (x, y, z)) == [2x 1 0; 4 0 2z]
 
+    @testset "Differentiate empty polynomial" begin
+        p = x^0 - 1
+        @test iszero(@inferred differentiate(p, x))
+        @test all(iszero, @inferred differentiate(p, [x, y]))
+    end
+
     @testset "differentiation with Val{}" begin
         @test @inferred(differentiate(x, x, Val{0}())) == x
         @test @inferred(differentiate(x, x, Val{1}())) == 1