Finite fields to new coercion model

[roed314]

Moves finite fields to the new coercion model. Patches have been moved to #8334, so do not apply the patches from this ticket.

Depends on #8218, #8332, #7880 and #7883. Prerequisite for #8334, #8335, #9887.

Component: algebra

Author: David Roe

Reviewer: David Loeffler

Issue created by migration from https://trac.sagemath.org/ticket/8333

[roed314]

Attachment: 8333_parent_init.patch.gz

[roed314]

comment:1

Attachment: 8333_finite_fields_to_new_coercion.patch.gz

The two patches can be applied in either order.

[roed314]

comment:2

Part of a series:

8218 -> 8332 -> 7880 -> 7883 -> 8333 -> 8334 -> 8335

I tried to make each of these mostly self contained, with doctests passing after every ticket, but I didn't entirely succeed. If you're reviewing one of these tickets, applying later tickets will hopefully fix doctest failures that you're seeing.

[roed314]

Description changed:

--- 
+++ 
@@ -1 +1,3 @@
 Moves finite fields to the new coercion model.
+
+Depends on 8218, 8332 and probably 7880 and 7883.

[loefflerd]

comment:4

Some strange things going on here. I installed the patches on 4.3.4.rc0 with the preceding patches in the series applied.

(1) It builds fine, but Sage won't start because the patched finite_field_prime_modn.py contains the line

from sage.rings.integer_mod_ring import IntegerModRing_generic

and that file has been removed by #8218.

(2) There is also a problem in element_ext_pari.py caused by the line

elif isinstance(value, FreeModuleElement):

being used without FreeModuleElement being imported first.

(3) Next up, there's another issue in element_ntl_gf2e caused by trying to import is_FiniteField from the wrong place.

(4) I'm getting a bunch of identical errors relating to the Singular library -- it says

 File "/home/masiao/sage-4.3.4.rc0/local/lib/python/site-packages/sage/interfaces/singular.py", line 672, in has_coerce_map_from_impl
        raise NotImplementedError

(5) Something weird is going on in sage/modular/dirichlet.py which causes an infinite recursion error when reducing an element of a number field modulo a prime; this may well be dealt with by #8334, I haven't checked. Same in three places in sage/schemes/elliptic_curves/ell_point.py and a bunch of other elliptic curves modules, and in sage/rings/residue_field.py

(6) The patch changes a whole load of doctests in sage/libs/flint/zmod_poly_linkage for no apparent reason, and thus causes them to fail. (Are you running a newer FLINT version on your development machine?)

(7) Various errors in the rings/finite_rings directory, e.g. this one:

File "/home/masiao/sage-4.3.4.rc0/local/lib/python/site-packages/sage/rings/finite_rings/finite_field_ext_pari.py", line 580, in _coerce_map_from_
        elif self.degree() % K.degree() == 0:
    NameError: global name 'K' is not defined

Most of these are trivial, but (4) is beyond my ability to fix. I'm sorry, but that's definitely a "needs work".

[loefflerd]

comment:5

Ah, I see what's going on. Most of these are fixed by the patch 7585_12_1_fixes.patch at #8334. But that is dependent on #7883, which needs some substantial work.

David, I suggest you do one of the following things:

• Fix Added some functionality to ideals #7883 as robertwb and I have suggested; once that has a positive review then we can go on and review this ticket and Improvements to residue fields #8334 together.

• Back-port the fixes from Improvements to residue fields #8334 that belong here, and then I will happily review it independently of Added some functionality to ideals #7883 and Improvements to residue fields #8334.

David

[roed314]

comment:6

I've addressed your and Robert's suggestions on #7883 I think. Apply these two patches after the patches at #7883 and before the patches at #8334. Doctests won't pass until you apply the patches at #8334. But all three are ready for review. Sorry for the delay.