Improve is_injective()/is_surjective() for coercions of quotient rings

[saraedum]

This should return True

sage: R.<x> = ZZ[]
sage: S.<x> = QQ[]
sage: S.quo(x^2 + 1).coerce_map_from(R.quo(x^2 + 1)).is_injective()

Generally, if R→S is injective/surjective then the quotient is.

[git]

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

​64776a9

Implement is_injective/is_surjective for coercions of quotient rings

[abourgeois]

All doctests pass on src/sage/rings/polynomial/polynomial_quotient_ring.py However, when running the doctests on src/sage/rings, I believe it requires #23204, based on the dependencies of #23482 and #23483.

[git]

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

​d27262a

Fix _richcmp_

[saraedum]

New commits:

​d27262a

Fix _richcmp_

---

New commits:

​d27262a

Fix _richcmp_

[chapoton]

• missing enpty line after EXAMPLES::

[saraedum]

Replying to chapoton:

• missing enpty line after EXAMPLES::

Is this fixed already? I could not find the EXAMPLES:: you are referring to.

[chapoton]

indeed. But there is the same issue in richcmp as in #23185

[git]

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

​46cb2f9

Implement _richcmp_ as discussed in 23185

[chapoton]

does not apply

[git]

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

​e2c1e36

Merge branch 'develop' into t/23190/23190

[saraedum]

File "src/sage/rings/polynomial/polynomial_quotient_ring.py", line 1868, in sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_coercion.is_surjective
Failed example:
    f.is_surjective()
Exception raised:
    Traceback (most recent call last):
      File "/tmp/sage-patchbot/sage/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 509, in _run
        self.compile_and_execute(example, compiler, test.globs)
      File "/tmp/sage-patchbot/sage/local/lib/python2.7/site-packages/sage/doctest/forker.py", line 872, in compile_and_execute
        exec(compiled, globs)
      File "<doctest sage.rings.polynomial.polynomial_quotient_ring.PolynomialQuotientRing_coercion.is_surjective[2]>", line 1, in <module>
        f.is_surjective()
      File "/tmp/sage-patchbot/sage/local/lib/python2.7/site-packages/sage/rings/polynomial/polynomial_quotient_ring.py", line 1882, in is_surjective
        constant_map_is_surjective = self.codomain().base_ring().coerce_map_from(self.domain().base_ring()).is_surjective()
      File "sage/categories/map.pyx", line 1204, in sage.categories.map.Map.is_surjective (build/cythonized/sage/categories/map.c:9316)
        raise NotImplementedError(type(self))
    NotImplementedError: <type 'sage.categories.morphism.IdentityMorphism'>

[git]

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

​944e05e

Merge branch 'develop' into t/23190/23190

[saraedum]

Somehow #23482 is not in develop yet, that's why the tests fail.

[mderickx]

I think the mathematical content of the statement if R -> S is injective then the quotient is, is no true. A counter example is for example ZZ['x'].quo(2) == GF(2)['x'] which does not inject into QQ['x'].quo(2) == 0. This example is not a pathology of 2 being in the constant field, it fails for any polynomial whose content is not a unit.

A nice sufficient condition for injectivity is that the polynomial be monic (or more generally if its leading coefficient is a unit).

There are no problems with surjectivity.

[saraedum]

Thanks for catching that one. You are right of course. Fixed now.

[git]

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

​19aee53

Fix is_injective

[git]

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

​282ea20

Do not test is_jnjective() for non-unit leading coefficient

[mderickx]

Ok the code looks fine now. If you can rewrite the extremely long lines such as:

if self.domain().modulus().change_ring(self.codomain().base_ring()) == self.codomain().modulus() and self.domain().modulus().leading_coefficient().is_unit():

and all the doctests pass. Then this ticket gets a positive review from me. P.s. In reviewing this ticket I also found some mathematically incorrect behaviour of quotients of univariate polynomials rings. I created a separate ticket for this: #23621

[git]

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

​8a1e18b

break long lines

[saraedum]

I only found that one line that's extremely long. For the others that are somewhat long I don't think there is a good position that calls for breaking them there. (But if you insist, I can break them of course.)

---

New commits:

​8a1e18b

break long lines

[chapoton]

a question to abourgeois : should we write "Adele" or "Adèle" ?

[abourgeois]

Replying to chapoton:

a question to abourgeois : should we write "Adele" or "Adèle" ?

I usually sign my name with the accent, but I don't really have a preference in writing (some of my legal documents omit the accent).

[mderickx]

Ok, looks good to me.