Change impl to implementation in sage.rings.finite_rings with deprecation

[Newtech66]

📚 Description

Changed all instances of impl to implementation in sage.rings.finite_rings. Also added deprecation warning for impl in finite_field_constructor.py.

Fixes #30507.

📝 Checklist

• The title is concise, informative, and self-explanatory.
• The description explains in detail what this PR is about.
• I have linked a relevant issue or discussion.
• I have created tests covering the changes.
• I have updated the documentation accordingly.

⌛ Dependencies

[roed314]

Generally looks good; I've approved the test run and once tests pass I'm happy with this PR.

[mkoeppe]

Lots of doctests are failing:

      File "sage/categories/functor.pyx", line 382, in sage.categories.functor.Functor.__call__
        y = self._apply_functor(self._coerce_into_domain(x))
      File "/__w/sage/sage/src/sage/categories/pushout.py", line 505, in _apply_functor
        R = c(R)
      File "sage/categories/functor.pyx", line 382, in sage.categories.functor.Functor.__call__
        y = self._apply_functor(self._coerce_into_domain(x))
      File "/__w/sage/sage/src/sage/categories/pushout.py", line 3290, in _apply_functor
        return R.extension(self.polys[0], names=self.names[0], embedding=self.embeddings[0],
    KeyError: 'implementation'

[Newtech66]

There seems to be an issue with this bit of code:

sage: K = GF(2^3,'a')
sage: F,O = K.construction()
sage: F(O)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
Cell In [43], line 1
----> 1 F(O)

File ~/sage/src/sage/categories/functor.pyx:382, in sage.categories.functor.Functor.__call__()
    380 if is_Morphism(x):
    381     return self._apply_functor_to_morphism(x)
--> 382 y = self._apply_functor(self._coerce_into_domain(x))
    383 if not ((y in self.__codomain) or (y in self.__codomain.Homsets())):
    384     raise TypeError("%s is ill-defined, since it sends x (=%s) to something that is not in %s." % (repr(self), x, self.__codomain))

File ~/sage/src/sage/categories/pushout.py:3290, in AlgebraicExtensionFunctor._apply_functor(self, R)
   3288     return R.residue_field(R*self.residue, names=tuple(self.names))
   3289 if len(self.polys) == 1:
-> 3290     return R.extension(self.polys[0], names=self.names[0], embedding=self.embeddings[0],
   3291                        structure=self.structures[0], prec=self.precs[0],
   3292                        implementation=self.implementations[0],
   3293                        latex_names=self.latex_names[0], **self.kwds)
   3294 return R.extension(self.polys, names=self.names, embedding=self.embeddings,
   3295                    structure=self.structures, prec=self.precs,
   3296                    implementation=self.implementations,
   3297                    latex_names=self.latex_names, **self.kwds)

TypeError: FiniteField_prime_modn_with_category.extension() got multiple values for keyword argument 'implementation'

The problem is that when F,O = K.construction() is called, F (an instance of AlgebraicExtensionFunctor) gets a keyword implementation: givaro (lines 1419-1458 in sage/rings/finite_rings/finite_field_base.pyx) from K (which is of type class <sage.rings.finite_rings.finite_field_givaro.FiniteField_givaro_with_category>). Then when F(O) is called, the function _apply_functor passes implementation again along with the previous one and now there is a clash.

How to resolve this? It doesn't look like F needs this keyword, so perhaps it should be deleted in __init__? I am referencing line 3475 in sage/categories/pushout.py for this suggestion.

[Newtech66]

But the implementation needs to be taken into account. Adding the passed implementation keyword to self.implementations seems to fix the problem.

[Newtech66]

All previously failing doctests are now passing on my system.

[Newtech66]

Can it be reviewed?

[kwankyu]

Workflows are awaiting approval from a maintainer.

[github-actions]

Documentation preview for this PR (built with commit 95e3bc6; changes) is ready! 🎉

[kwankyu]

L3553,3554 could also be deleted, I think.

[Newtech66]

Removed.