Antidifferentiation (primitive)

[bmxam]

With this PR, I propose to introduce a function to get the antiderivative of multivariate polynomial. Note that the word primitive, (more natural in my native language), is already used by the Julia language; hence the antiderivative name. An associated PR in TypedPolynomials is proposed.

I tried to copy what is currently done for differentiate. Except for RationalPoly, which are not always possible to antidifferentiate with polynoms. I provided some unit tests as well.

With this new function, it would then be easy to integrate a multivariate polynomial on (simple) geometries such as lines, quads, cubes etc.

Note : for personal reasons, I may be absent in the next few weeks. Don't hesitate to continue the PR process "without me".

[bmxam]

I see that the no-reg is failing because (as I understand it) it tries to apply antidifferentiate with DynamicPolynomials, which is not implemented. How can I fix this problem?

[blegat]

We need to add the definition of antidifferentiate first, release MultivariatePolynomials, then add it to DynamicPolynomials, then release DynamicPolynomials and then add the tests in MultivariatePolynomials

[bmxam]

We need to add the definition of antidifferentiate first, release MultivariatePolynomials, then add it to DynamicPolynomials, then release DynamicPolynomials and then add the tests in MultivariatePolynomials

Alright. I will propose a commit without any tests.

[blegat]

I am a bit concerned about defaulting to Float64, this might also be used with polynomials on Rational{BigInt} for instance, I would use Rational{Int} as it is more neutral so it will preserve the type of the polynomial it is used with

julia> typeof(1.0 * (1 // 2))
Float64

julia> typeof((big(1)) * (1 // 2))
Rational{BigInt}

julia> typeof((big(1) // big(2)) * (1 // 2))
Rational{BigInt}

[bmxam]

you're right, I fixed it in my last commit (c34bb38)

[blegat]

Note that the word primitive, (more natural in my native language), is already used by the Julia language; hence the antiderivative name. An associated PR in TypedPolynomials is proposed.

I am also french-speaking so primitive is more natural for me as well but let's follow wikipedia: https://en.wikipedia.org/wiki/Antiderivative which uses antidifferentiate

[bmxam]

We need to add the definition of antidifferentiate first, release MultivariatePolynomials, then add it to DynamicPolynomials, then release DynamicPolynomials and then add the tests in MultivariatePolynomials

Alright. I will propose a commit without any tests.

(done in c34bb38)

[blegat]

Could you add some tests ?

[bmxam]

We need to add the definition of antidifferentiate first, release MultivariatePolynomials, then add it to DynamicPolynomials, then release DynamicPolynomials and then add the tests in MultivariatePolynomials

Hi Benoît, as I understand the tests will be added later. Or there is something I didn't understand?

[blegat]

Indeed, sorry, I forgot that part, let's merge then