add fmpz_poly_decompose [WIP]

[tthsqe12]

This is only intended to get some feed back on the interface. If you actually want to decompose a polynomial into indecomposables, you would have to call this in a loop.

[fredrik-johansson]

Seems like a function that takes care of the looping would be useful. Presumably, you could try mod p decompositions to rule out cases?

Related to this, have you thought about:

• Multivariate decomposition
• Common subexpression elimination / converting a multivariate polynomial to an optimized straight-line program (like Maple's codegen/optimize https://www.maplesoft.com/support/help/Maple/view.aspx?path=codegen%2Foptimize)

[tthsqe12]

I think neither of these belong in flint. The former seems too hard, and @rfourquet should have something for the latter with slp's. As for univariate decomposition, I hope I designed it to fail as quickly as possible if the decomp does not exist. Will require testing

[fredrik-johansson]

It would be useful to have a fmpz slp representation in flint as an intermediate representation for evaluation/composition (here I'm just thinking of a linear-time conversion to slp form, not expensive optimizations). For example, I could use that to evaluate an fmpz_mpoly at fmpq, arb, acb or fmpz_mpoly_q arguments.

[fredrik-johansson]

If anyone is interested, it should be straightforward to rebase this PR and maybe implement this:

If you actually want to decompose a polynomial into indecomposables, you would have to call this in a loop.