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Antidifferentiate #81

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1 change: 1 addition & 0 deletions src/TypedPolynomials.jl
Original file line number Diff line number Diff line change
Expand Up @@ -25,6 +25,7 @@ export @polyvar,
variables,
terms,
differentiate,
antidifferentiate,
subs

include("types.jl")
Expand Down
35 changes: 35 additions & 0 deletions src/calculus.jl
Original file line number Diff line number Diff line change
Expand Up @@ -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
28 changes: 28 additions & 0 deletions test/calculus.jl
Original file line number Diff line number Diff line change
Expand Up @@ -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
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These can be moved to MultivariatePolynomials/test/differentiation.jl

@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
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These can be moved to MultivariatePolynomials/test/allocations.jl

@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