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.

Depends on #23485
Depends on #23484
Depends on #23483
Depends on #23482

Component: commutative algebra

Keywords: sd86.5, sd87

Author: Julian Rüth

Branch/Commit: 8a1e18b

Reviewer: Adele Bourgeois, Maarten Derickx

Issue created by migration from https://trac.sagemath.org/ticket/23190

[roed314]

Changed keywords from sd86.5 to sd86.5, sd87

[saraedum]

Branch: u/saraedum/improve_is_injective___is_surjective___for_coercions_of_quotient_rings

[saraedum]

Changed branch from u/saraedum/improve_is_injective___is_surjective___for_coercions_of_quotient_rings to u/saraedum/23190

[sagetrac-git]

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

64776a9

Implement is_injective/is_surjective for coercions of quotient rings

[sagetrac-git]

Commit: 64776a9

[saraedum]

Dependencies: #23485, #23484, #23483, #23482

[sagetrac-abourgeois]

comment:10

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.

[sagetrac-abourgeois]

Reviewer: Adele Bourgeois

[saraedum]

Author: Julian Rüth

[saraedum]

Work Issues: failing doctest

[sagetrac-git]

Changed commit from 64776a9 to d27262a

[sagetrac-git]

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

d27262a

Fix _richcmp_

[saraedum]

Changed work issues from failing doctest to none

[saraedum]

New commits:

d27262a

Fix _richcmp_

---

New commits:

d27262a

Fix _richcmp_

[fchapoton]

comment:16

• missing enpty line after EXAMPLES::

[saraedum]

comment:17

Replying to @fchapoton:

• missing enpty line after EXAMPLES::

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

[fchapoton]

comment:18

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

[sagetrac-git]

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

46cb2f9

Implement `_richcmp_` as discussed in 23185

[sagetrac-git]

Changed commit from d27262a to 46cb2f9

[fchapoton]

comment:20

does not apply

[sagetrac-git]

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

944e05e

Merge branch 'develop' into t/23190/23190

[sagetrac-git]

Changed commit from e2c1e36 to 944e05e

[saraedum]

Changed work issues from failing doctest to none

[saraedum]

comment:26

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

[koffie]

comment:27

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]

comment:28

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

[sagetrac-git]

Changed commit from 944e05e to 19aee53

[sagetrac-git]

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

19aee53

Fix is_injective

[sagetrac-git]

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

282ea20

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

[sagetrac-git]

Changed commit from 19aee53 to 282ea20

[koffie]

comment:31

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():

in such a way that they comfortably fit on a reasonable screen 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

[sagetrac-git]

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

8a1e18b

break long lines

[sagetrac-git]

Changed commit from 282ea20 to 8a1e18b

[saraedum]

comment:33

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

[saraedum]

Changed reviewer from Adele Bourgeois to Adele Bourgeois, Maarten Derickx

[fchapoton]

comment:35

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

[sagetrac-abourgeois]

comment:36

Replying to @fchapoton:

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).

[koffie]

comment:37

Ok, looks good to me.

[vbraun]

Changed branch from u/saraedum/23190 to 8a1e18b