Add antidifferentiation for polynomials

src/anti_diff.jl

@@ -8,3 +8,19 @@ function MP.antidifferentiate(m::Monomial{V,M}, x::Variable{V,M}) where {V,M}
         Monomial(MP.variables(m), z) / (m.z[i] + 1)
     end
 end
+
+function MP.antidifferentiate(p::Polynomial{V,M,T}, x::Variable{V,M}) where {V,M,T}
+    i = something(findfirst(isequal(x), MP.variables(p)), 0)
+    S = typeof(zero(T) * 0)
+    if iszero(i)
+        x * p
+    else
+        Z = copy.(p.x.Z)
+        a = Vector{S}(undef, length(p.a))
+        for j in 1:length(Z)
+            a[j] = p.a[j] / (Z[j][i] + 1)
+            Z[j][i] += 1
+        end
+        Polynomial(a, MonomialVector(MP.variables(p), Z))
+    end
+end

test/poly.jl

@@ -81,6 +81,22 @@
         @inferred polynomial(2.0u, Int)
     end
 
+    @testset "Antiderivative" begin
+        @polyvar x y
+
+        p = (x^2 + 4*y^3)
+        pi = DynamicPolynomials.antidifferentiate(p, y)
+        @test pi == (x^2*y + y^4)
+
+        p = 2*y
+        pi = DynamicPolynomials.antidifferentiate(p, y)
+        @test pi == y^2
+
+        p = x^2
+        pi = DynamicPolynomials.antidifferentiate(p, y)
+        @test pi == x^2*y
+    end
+
     @testset "Evaluation" begin
         @polyvar x y
         @test (x^2 + y^3)(2, 3) == 31