Add antidifferentiation

[chrhansk]

This patch adds an implementation of the antidifferentiate function for both monomials and polynomials (fixing #157).

The function antidifferentiate(p, x) works by either returning the product p*x if p has no term with variable x, or by incrementing the powers and adjusting the coefficients to match (thereby always ensuring that the antiderivative evaluates to zero whenever x is zero).

I included some basic unit tests as well. I did not run JuliaFormatter.jl over the codebase, since numerous other files are not formatted according to those formatting rules...

Let me know if anything is missing. If this lands, I would appreciated a new version to be used in my own project.

[blegat]

Looks very good thanks. Maybe we should go for Rational{Int} if the current coefficient type is Int ? So create some custom _div that uses / if AbstractFloat and // otherwise. Note that 1 // 2 is used here
https://github.com/JuliaAlgebra/MultivariatePolynomials.jl/blob/master/src/antidifferentiation.jl#L30
so it's consistent with that

[chrhansk]

Done.

[chrhansk]

Is there anything else needed or is this ready to merge?

[blegat]

Can you use coefficient_type instead ?

[chrhansk]

I was indeed unaware of the existence of that particular function. The problem should be fixed by now.

I also noticed another aspect regarding the monomials: The antidifferentiation of a monomial yields a term with a Float64 type. We could make this a Rational{Int} instead (similarly to the polynomial case). What is your opinion on this?

[blegat]

Yes, this should also be Rational{Int}

[chrhansk]

OK, I adjusted the implementation accordingly.

[blegat]

Thanks, let's wait to see the CI results but looks good to me