[Draft] use algebraic number for reals

[bobot]

ocaml-flint version 0.3 is needed

[bobot]

@Gbury can you take a look at f5700bc to see if the way and place the new construct have been introduced is correct. Note that it is not anymore (root-of-with-ordering (p_0 p_1 ... p_n) i) but (root-of-with-ordering (coeffs p_0 p_1 ... p_n) i) in order to respect the syntax of terms.

[Gbury]

The addition of the new primitive looks fine (modulo some renaming as per my comment).

[Gbury]

Looking at the CI, and I'm wondering: is calcium not available on windows ?

[bobot]

I have not made the effort of making it work there, but I have also not actively forbid it so I don't yet understand.

[bobot]

Are the package updated in the windows CI? Perhaps this should be added: opam repo add upstream https://opam.ocaml.org --rank 2 --all-switches --set-default

[bobot]

I think it is just because the original windows repo stop updating last year: https://ocaml.org/docs/ocaml-on-windows#opam-repository-mingw . I haven't been able to test adding the current one in my virtual machine. (ocaml-ci can also be a good CI since it is the one used by opam) (EDIT: sorry for the repetition, github slowly updated the page 🤦 )

[Gbury]

yeah, it's not the first time the windows CI has had problems because the repo used by setup-ocaml for windows runner is old and not updated regularly... I'll try and see what solutions there are (including manually adding an up-to-date repo as you suggested)

[Gbury]

I pushed a few changes, mainly some refactoring and documentation, as well as proper errors instead of the invalid_arg. The code is good for merging, but we need to figure out how to make CI runs succeed; the installation of flint/calcium takes way too long: 6h+ on the windows CI which end up being forcefully shut down before completion. Ideally, the flint/calcium/arb packages could try and make use of depexts to rely on systems binary packages for the big C (or C++ ?) libraries.

[Gbury]

ocaml/opam-repository#24509 might solve the CI problems. Will try again once it is merged.

[Gbury]

With the upgrade to flint version 3.x, I think we now have a much better windows compatibility story, @bobot do you think you have the time to update this PR ? ELse I'll try and find the time to bring it up to date so that I can merge it.