implement is_squarefree for p-adic rings

[saraedum]

Currently, this does not work

sage: R.<a> = ZqFM(9)
sage: a.is_squarefree()
AttributeError

CC: @roed314

Component: padics

Author: Julian Rüth

Branch/Commit: 3875877

Reviewer: David Roe

Issue created by migration from https://trac.sagemath.org/ticket/23525

[saraedum]

Branch: u/saraedum/implement_is_squarefree_for_p_adic_rings

[saraedum]

comment:2

I did not run any doctests yet (still rebuilding sage.)

---

New commits:

8051942

is_squarefree() for p-adics

[saraedum]

Author: Julian Rüth

[saraedum]

Commit: 8051942

[roed314]

comment:3

Maybe we should just raise a TypeError for fields? QQ and number fields don't define an is_squarefree method (though elements of orders don't either). This may be another case where we can return a technically correct answer but it's most likely not what the user was expecting.

[saraedum]

comment:4

I think it makes sense to return mathematically correct answers even if they are trivial. It means that you can write algorithms without checking for trivial cases. E.g., we do this already to determine whether a polynomial is squarefree: first we check whether it's content is squarefree. A trivial check over fields, but still the correct thing to do. So currently we need to protect this check with a self.base_ring() in Fields() to work around the fact that Fields.ElementMethods does not implement is_squarefree() [which it imho should.]

[saraedum]

comment:5

PS: I think it really depends on who are you writing code for. Beginners will be surprised that

sage: x = 8/2; x
4
sage: x.is_squarefree()
True

but eventually you are going to learn that parents are very important in Sage…

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

3875877

simplify field case

[sagetrac-git]

Changed commit from 8051942 to 3875877

[roed314]

comment:7

Okay, we had some more discussion on IRC and I'm fine with this now. Positive review once tests pass.

[roed314]

comment:8

The only failure is the intermittent

sage -t --long src/sage/rings/fraction_field_FpT.pyx  # 3 doctests failed

which is already addressed by #23554.

[roed314]

Reviewer: David Roe

[vbraun]

Changed branch from u/saraedum/implement_is_squarefree_for_p_adic_rings to 3875877