Antidifferentiate

src/TypedPolynomials.jl

@@ -25,6 +25,7 @@ export @polyvar,
        variables,
        terms,
        differentiate,
+       antidifferentiate,
        subs
 
 include("types.jl")

src/calculus.jl

@@ -37,3 +37,38 @@ function _diff(m::Monomial{Vars},
         end
     end, Val{N}()))
 end
+
+MP.antidifferentiate(v1::V, v2::V) where {V <: Variable} = v1*v2/2
+MP.antidifferentiate(v1::Variable, v2::Variable) = v1 * v2
+
+function MP.antidifferentiate(m::Monomial{Vars}, v::V) where {Vars, V <: Variable}
+    if inmonomial(v, Vars...)
+        return _antidiff(m, v)
+    else
+        # Insert `v` in the monomial
+        return m * v
+    end
+end
+
+_antidiff(m::Monomial, v::Variable) = _antidiff(m, exponents(m), v)
+
+function _antidiff(::Monomial{Vars},
+               exponents::NTuple{N, Integer},
+               v::Variable) where {Vars, N}
+    vi = find_variable_index(v, Vars)
+    new_m = Monomial{Vars,N}(
+        ntuple(i -> begin
+                if i == vi
+                    (exponents[i] == 0) ? 1 : exponents[i] + 1
+                else
+                    exponents[i]
+                end
+            end,
+            Val{N}()
+        )
+    )
+    # Remark : as `exponents` are imposed to be `Integer` according to
+    # the method signature, we can use the Rational{Int} type here for the
+    # coefficient
+    return (1 // (exponents[vi] + 1)) * new_m
+end

test/calculus.jl

@@ -25,3 +25,31 @@
 
     @test @inferred(differentiate(1, x)) == 0
 end
+
+@testset "antiderivatives" begin
+    @polyvar x y z
+
+    @test @inferred(antidifferentiate(x, x)) == 1//2*x^2
+    @test @inferred(antidifferentiate(x, y)) == x*y
+    @test @inferred(antidifferentiate(y, x)) == x*y
+    @test @inferred(antidifferentiate(x^2, x)) == 1//3*x^3
+    @test @inferred(antidifferentiate(x^2, y)) == x^2*y
+    @test @inferred(antidifferentiate(x^2 * y^3, y)) == x^2 * 1//4*y^4
+    @test @inferred(antidifferentiate(x^2 * y^3, x)) == x^3 * 1//3*y^3
+    @test @inferred(antidifferentiate(x^2 * y^3, z)) == x^2 * y^3 * z
+    @test @inferred(antidifferentiate(3x^2, x)) == x^3
+    @test @inferred(antidifferentiate(3x^2 * y^0, y)) == 3x^2 * y
+    @test @inferred(antidifferentiate(3 * x^2 + 2 * x + 1, x)) == x^3 + x^2 + x
+
+    @test @inferred(exponents(antidifferentiate(x^0,x))==(1,))
+    @test @inferred(exponents(antidifferentiate(x^0*y*z^2,x))==(1,1,2))
+
+    m = x^2
+    @test @wrappedallocs(antidifferentiate(m, x)) == 0
+    @test @wrappedallocs(antidifferentiate(m, y)) == 0
+    m = x^2 * y^3
+    @test @wrappedallocs(antidifferentiate(m, x)) == 0
+    @test @wrappedallocs(antidifferentiate(m, y)) == 0
+
+    @test @inferred(antidifferentiate(1, x)) == x
+end