Random failure in ell_field.py with division_field

[jhpalmieri]

Steps To Reproduce

This raises an error:

sage: F.<a> = GF(592337197)
sage: E = EllipticCurve([F(341280459), F(489478549), F(203134672), F(127259459), F(366459012)])
sage: E
Elliptic Curve defined by y^2 + 341280459*x*y + 203134672*y = x^3 + 489478549*x^2 + 127259459*x + 366459012 over Finite Field of size 592337197
sage: E.division_field(3)

As a result, this doesn't pass for me (OS X):

sage -t --long --random-seed=46499345266195225323927627332877868800 src/sage/schemes/elliptic_curves/ell_field.py

Expected Behavior

The test should pass.

Actual Behavior

An error is raised:

TypeError: unable to convert Identity endomorphism of Finite Field of size 592337197 to an element of Finite Field of size 592337197

Additional Information

No response

Environment

- OS X 13.6.1, Intel, plus various `homebrew` packages
- Sage version 10.3.beta0

Checklist

• I have searched the existing issues for a bug report that matches the one I want to file, without success.
• I have read the documentation and troubleshoot guide

[dimpase]

@JohnCremona

[DaveWitteMorris]

This seems to be a new bug. I did not get an error (and the specified doctests passed) with v10.2 on intel MacOS 13.6:

sage: E.division_field(3)
Finite Field of size 592337197

But I get the TypeError now that I have upgraded to 10.3b0.

[JohnCremona]

I will take a look. Not today

[dimpase]

Probably related to Flint upgrade in #35848

[mkoeppe]

This failure is not specific to macOS. Also shows up randomly in the conda CI on Linux - https://github.com/sagemath/sage/actions/runs/7259211723/job/19837970698?pr=36877#step:11:8314

[yyyyx4]

Minimal failing example:

sage: F = GF(11)
sage: phi = Hom(F,F).an_element()
sage: R.<x,y> = F[]
sage: x.change_ring(phi)

Part of the issue is that identity finite-field embeddings are returned as a generic IdentityMorphism:

sage: type(Hom(GF(11), GF(11)).an_element())
<class 'sage.categories.morphism.IdentityMorphism'>
sage: type(Hom(GF(11), GF(11^2)).an_element())
<class 'sage.rings.finite_rings.hom_prime_finite_field.FiniteFieldHomomorphism_prime'>

...which then proceeds to cause trouble somewhere in the coercion system.

[tornaria]

Can you add division_field to the title. I reported this in #35936 because this one didn't pop up in search.

My example is:

EllipticCurve(GF(528238639), [78525647, 395630016, 427518312, 245441800, 351879008]).division_field(3)

[kwankyu]

Minimal failing example:

sage: F = GF(11)
sage: phi = Hom(F,F).an_element()
sage: R.<x,y> = F[]
sage: x.change_ring(phi)

What do you mean? Is this supposed to work? phi is not a ring. So failure is expected.

[yyyyx4]

The input for .change_ring() can be either a ring or a ring morphism. The documentation says "R" -- a ring or morphism and shows an example where it works. In this case it also works for ring morphisms which aren't the IdentityMorphism.

(Edit) Example for your convenience:

sage: F = GF(11)
sage: phi = Hom(F, F.extension(2)).an_element()
sage: R.<x,y> = F[]
sage: x.change_ring(phi)
x
sage: x.change_ring(phi).parent()
Multivariate Polynomial Ring in x, y over Finite Field in z2 of size 11^2

[kwankyu]

It makes sense. Thanks.

Then it remains to spot the code that is responsible in dealing with the morphism input.

[yyyyx4]

I think we should also consider the possibility that having a generic IdentityMorphism class is not very useful and it'd be better to instead construct an identity morphism of the same type as all the other morphisms in that category.

[kwankyu]

Generic IdentityMorphism class itself has no fault, but the identity morphism in Hom(GF(11), GF(11)) should be a ring homomorphism, that is, an instance of RingHomomorphism or something. This seems a bug of Hom.

[kwankyu]

I traced the code. At some point, isinstance(x, morphism.RingHomomorphism_im_gens) returns False for x being Identity endomorphism of Finite Field of size 11 and type(x) <class 'sage.categories.morphism.IdentityMorphism'>

[kwankyu]

--- a/src/sage/rings/polynomial/multi_polynomial.pyx
+++ b/src/sage/rings/polynomial/multi_polynomial.pyx
@@ -878,9 +878,9 @@ cdef class MPolynomial(CommutativePolynomial):
             [x*y]
         """
         if isinstance(R, Map):
-        #if we're given a hom of the base ring extend to a poly hom
+            # if we're given a hom of the base ring, extend to a hom of the polynomial ring
             if R.domain() == self.base_ring():
-                R = self.parent().hom(R, self.parent().change_ring(R.codomain()))
+                R = self.parent().hom(self.parent().change_ring(R.codomain()), base_map=R)
             return R(self)
         else:
             return self.parent().change_ring(R)(self.dict())

This seems to fix the original bug (without "fixing identity morphism").

[enriqueartal]

Can it be related to #36472?

[kwankyu]

No. That is for ideals. This is for polynomials.

[kwankyu]

The fix #37159 is ready for review.