Iojea master (#616)

* Include a method for derivative of constant `ImmutableDensePolynomial` (N=1). The method returns the zero `ImmutableDensePolynomial. This is a possible fix of a bug, since previously derivative of an `ImmutablePolynomial` returned an unusable polynomial of type `ImmutablePolynomial{Union{},:x,0}`.

* Improved derivative for constant `ImmutablePolynomial`. `derivative(p)` now returns `zero(p)`.

* subtract, not add; add simple tests

* test display

---------

Co-authored-by: Ignacio Ojea <[email protected]>

Author: jverzani

src/polynomials/standard-basis/immutable-polynomial.jl

@@ -145,8 +145,6 @@ derivative(p::ImmutableDensePolynomial{B,T,X,0}) where {B<:StandardBasis,T,X} =
 derivative(p::ImmutableDensePolynomial{B,T,X,1}) where {B<:StandardBasis,T,X} = zero(p)
 
 function derivative(p::ImmutableDensePolynomial{B,T,X,N}) where {B<:StandardBasis,T,X,N}
-    N == 0 && return p
-    N == 1 && return zero(p)
     hasnan(p) && return ImmutableDensePolynomial{B,T,X,1}(zero(T)/zero(T)) # NaN{T}
     cs = ntuple(i -> i*p.coeffs[i+1], Val(N-1))
     R = eltype(cs)

test/StandardBasis.jl

@@ -1094,6 +1094,15 @@ end
         @test_throws ArgumentError derivative(pR, -1)
         @test integrate(P([1,1,0,0]), 0, 2) == 4.0
 
+        p₀, p₁, p₂ = zero(P), one(P), variable(P)
+        @test derivative(p₂) == p₁
+        @test derivative(p₁) == p₀
+        @test integrate(p₀, 1) == p₁
+        @test integrate(p₁) == p₂
+        if P != Polynomials.MutableSparseVectorPolynomial{Polynomials.StandardBasis}
+            @test repr(derivative(p₁)) == string(P)*"(0.0)" # #615 display issue
+        end
+
         P <: FactoredPolynomial && continue
 
         @testset for i in 1:10